Tootfinder

Lectures on stochastic sewing with applications
Oleg Butkovsky
https://arxiv.org/abs/2510.12165 https://arxiv.org/pdf/2510.12165

Lectures on stochastic sewing with applications
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to introduce the reader to stochastic sewing techniques and to show how they can be successfully applied to study various problems in stochastic analysis, including: regularization by noise for stochastic differential equations driven by Brownian motion or fractional Brownian motion, well-posedness of stochastic PDEs with irr…

Easy-to-Implement One-Step Schemes for Stochastic Integration
J. Woodfield, A. Lobbe
https://arxiv.org/abs/2510.12583 https://arxiv.org/pdf/2510.12583

Easy-to-Implement One-Step Schemes for Stochastic Integration
Convenient, easy to implement stochastic integration methods are developed on the basis of abstract one-step deterministic order $p$ integration techniques. The abstraction as an arbitrary one step map allows the inspection of easy to implement stochastic exponential time differencing Runge-Kutta (SETDRK), stochastic integrating factor Runge-Kutta (SIFRK) and stochastic RK (SRK) schemes. Such schemes require minimal modifications to existing deterministic schemes and converging to the Stratonov…

One Life to Learn: Inferring Symbolic World Models for Stochastic Environments from Unguided Exploration
Zaid Khan, Archiki Prasad, Elias Stengel-Eskin, Jaemin Cho, Mohit Bansal
https://arxiv.org/abs/2510.12088

One Life to Learn: Inferring Symbolic World Models for Stochastic Environments from Unguided Exploration
Symbolic world modeling requires inferring and representing an environment's transitional dynamics as an executable program. Prior work has focused on largely deterministic environments with abundant interaction data, simple mechanics, and human guidance. We address a more realistic and challenging setting, learning in a complex, stochastic environment where the agent has only "one life" to explore a hostile environment without human guidance. We introduce OneLife, a framework that models world…

Geometric Phase of Stochastic Oscillators
Yangyang Du
https://arxiv.org/abs/2509.10900 https://arxiv.org/pdf/2509.10900

Geometric Phase of Stochastic Oscillators
Several definitions of phase have been proposed for stochastic oscillators, among which the mean-return-time phase and the stochastic asymptotic phase have drawn particular attention. Quantitative comparisons between these two definitions have been done in previous studies, but physical interpretations of such a relation are still missing. In this work, we illustrate this relation using the geometric phase, which is an essential concept in both classical and quantum mechanics. We use properties…

Carleman Estimates and Controllability of Forward Stochastic Parabolic Equations with General Dynamic Boundary Conditions
Said Boulite, Abdellatif Elgrou, Lahcen Maniar, Abdelaziz Rhandi
https://arxiv.org/abs/2510.12345

Carleman Estimates and Controllability of Forward Stochastic Parabolic Equations with General Dynamic Boundary Conditions
We derive a new Carleman estimate for a general backward stochastic parabolic equation with dynamic boundary conditions, incorporating weak divergence source terms in both the bulk and surface equations. This estimate is obtained through two main steps: first, by refining a known Carleman estimate for backward stochastic parabolic equations to explicitly account for the dependence of the parameters on the final control time \(T\); second, by applying a duality technique to address weak divergen…

Localised solution of stochastic Schr\"odinger equation describing simultaneous continuous measurement of position and momentum
Daniel J. Bedingham
https://arxiv.org/abs/2509.11832

Localised solution of stochastic Schrödinger equation describing simultaneous continuous measurement of position and momentum
A stochastic Schrödinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum contingent on the uncertainty principle. The state is understood as that to which the particle tends after a period of continuous measurement. The solution takes the form of a wave packet of fixed Gaussian shape whose centre undergoes random motion in phase space. It…

Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
Jia-Qi Yang, Lei Shi
https://arxiv.org/abs/2509.11070 https://arxiv.org/pdf…

Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which admit discrete spectral decompositions, and (ii) diagonal kernels of the form $K(x,x')=k(x,x')T$, where $k$ is a scalar-valued kernel and $T$ is a positive operator on the output space. This broad setting induces expressive vector-valued reproducing kernel Hilbe…

Model Predictive Control with High-Probability Safety Guarantee for Nonlinear Stochastic Systems
Zishun Liu, Liqian Ma, Yongxin Chen
https://arxiv.org/abs/2509.11584 https://

Model Predictive Control with High-Probability Safety Guarantee for Nonlinear Stochastic Systems
We present a model predictive control (MPC) framework for nonlinear stochastic systems that ensures safety guarantee with high probability. Unlike most existing stochastic MPC schemes, our method adopts a set-erosion that converts the probabilistic safety constraint into a tractable deterministic safety constraint on a smaller safe set over deterministic dynamics. As a result, our method is compatible with any off-the-shelf deterministic MPC algorithm. The key to the effectiveness of our method…

Anonymous leadership and stochastic resonance in collectives of self-propelled robots
Manuel Dizenhaus, Franco De Simone, German A. Patterson
https://arxiv.org/abs/2510.12580 ht…

Anonymous leadership and stochastic resonance in collectives of self-propelled robots
We investigate the influence of an anonymous leader on a collective of self-propelled robots using Kilobot experiments and numerical simulations. A single leader alternated deterministically between clockwise and counterclockwise motion, while the other robots followed a stochastic majority rule. Although the leader does not change global order, it induces correlations with the collective response that peak at intermediate perturbation levels, resembling stochastic resonance. Simulations confir…

Large-Scale Curve Time Series with Common Stochastic Trends
Degui Li, Yu-Ning Li, Peter C. B. Phillips
https://arxiv.org/abs/2509.11060 https://arxiv.org/p…

Large-Scale Curve Time Series with Common Stochastic Trends
This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor model for the latent curves with common trends. A functional PCA technique is applied to estimate the common stochastic trends and functional factor loadings. Under some regularity conditions we derive the mean square convergence and limit distribution theory f…

Time Averaged Statistics of the 3D Stochastic Ladyzenskaya-Smagorinsky Equations
Wai-Tong Louis Fan, Ali Pakzad
https://arxiv.org/abs/2510.12004 https://ar…

Time Averaged Statistics of the 3D Stochastic Ladyzenskaya-Smagorinsky Equations
Due to the chaotic nature of turbulence, statistical quantities are often more informative than pointwise characterizations. In this work, we consider the stochastic Ladyzhenskaya-Smagorinsky equation driven by space-time Gaussian noise on a three-dimensional periodic domain. We derive a rigorous upper bound on the first moment of the energy dissipation rate and show that it remains finite in the vanishing viscosity limit, consistent with Kolmogorov's phenomenological theory. This estimate also…

Strong convergence rates of stochastic theta methods for index 1 stochastic differential algebraic equations under non-globally Lipschitz conditions
Lin Chen, Ziheng Chen, Jing Zhao
https://arxiv.org/abs/2509.11618

Strong convergence rates of stochastic theta methods for index 1 stochastic differential algebraic equations under non-globally Lipschitz conditions
This work investigates numerical approximations of index 1 stochastic differential algebraic equations (SDAEs) with non-constant singular matrices under non-global Lipschitz conditions. Analyzing the strong convergence rates of numerical solutions in this setting is highly nontrivial, due to both the singularity of the constraint matrix and the superlinear growth of the coefficients. To address these challenges, we develop an approach for establishing mean square convergence rates of numerical …

Stochastic restarting with multiple restart conditions
Johannes Aspman, Daniel Mastropietro, Jakub Marecek
https://arxiv.org/abs/2509.11809 https://arxiv.o…

Stochastic restarting with multiple restart conditions
We consider the mean first passage time (MFPT) for a diffusive particle in a potential landscape with the extra condition that the particle is reset to its original position with some rate r. We study non-smooth and non-convex potentials and focus on the case where the restart rate depends on the space coordinate. There, we show that it is beneficial to restart at a lower rate once you are closer to your intended target.

Statistical Guarantees for High-Dimensional Stochastic Gradient Descent
Jiaqi Li, Zhipeng Lou, Johannes Schmidt-Hieber, Wei Biao Wu
https://arxiv.org/abs/2510.12013 https://

Statistical Guarantees for High-Dimensional Stochastic Gradient Descent
Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide rigorous statistical guarantees for constant learning-rate SGD and ASGD in high-dimensional regimes. Our key innovation is to transfer powerful tools from high-dimensional time series to online learning. Specifically, by viewing SGD as a nonlinear autoregres…

Existence and uniqueness on $L^1$ solutions of multidimensional BSDEs with generators of stochastic one-sided Osgood type
Yuru Lai, Xinying Li, Shengjun Fan
https://arxiv.org/abs/2509.11927

Existence and uniqueness on $L^1$ solutions of multidimensional BSDEs with generators of stochastic one-sided Osgood type
By imposing an additional integrability condition on the first component of the solution, this paper establishes an existence and uniqueness result for $L^1$ solutions of multidimensional backward stochastic differential equations (BSDEs) with a general terminal time when the generator $g$ satisfies a stochastic one-sided Osgood condition along with a general growth condition in the state variable $y$, and a stochastic Lipschitz condition in the state variable $z$, extending and strengthening T…

A Stochastic Model for Illiquid Stock Prices and its Conclusion about Correlation Measurement
Erina Nanyonga, Juma Kasozi, Fred Mayambala, Hassan W. Kayondo, Matt Davison
https://arxiv.org/abs/2509.10553

A Stochastic Model for Illiquid Stock Prices and its Conclusion about Correlation Measurement
This study explores the behavioral dynamics of illiquid stock prices in a listed stock market. Illiquidity, characterized by wide bid and ask spreads affects price formation by decoupling prices from standard risk and return relationships and increasing sensitivity to market sentiment. We model the prices at the Uganda Securities Exchange (USE) which is illiquid in that the prices remain constant much of the time thus complicating price modelling. We circumvent this challenge by combining the M…

Distributed Stochastic Model Predictive Control with Temporal Aggregation for the Joint Dispatch of Cascaded Hydropower and Renewables
Luca Santosuosso, Sonja Wogrin
https://arxiv.org/abs/2510.11998

Distributed Stochastic Model Predictive Control with Temporal Aggregation for the Joint Dispatch of Cascaded Hydropower and Renewables
This paper addresses the real-time energy dispatch of a hybrid system comprising cascaded hydropower plants, wind, and solar units, jointly participating in the day-ahead energy market under inflow, renewable generation, and price uncertainties. Traditional scenario-based stochastic model predictive control (MPC) faces severe computational bottlenecks due to the complexity arising from the temporal, asset, and scenario dimensions of this control problem. To address this, we propose a novel cont…

Train Stochastic Non Linear Coupled ODEs to Classify and Generate
Stefano Gagliani, Feliciano Giuseppe Pacifico, Lorenzo Chicchi, Duccio Fanelli, Diego Febbe, Lorenzo Buffoni, Raffaele Marino
https://arxiv.org/abs/2510.12286

Train Stochastic Non Linear Coupled ODEs to Classify and Generate
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the dynamical system amounts to shaping the architecture of inter-nodes connection to steer the evolution towards the assigned equilibrium, as a function of the class to which the item - supplied as an initial condition - belongs to. Under the stochastic perspective, po…

Diffusion-DFL: Decision-focused Diffusion Models for Stochastic Optimization
Zihao Zhao, Christopher Yeh, Lingkai Kong, Kai Wang
https://arxiv.org/abs/2510.11590 https://…

Diffusion-DFL: Decision-focused Diffusion Models for Stochastic Optimization
Decision-focused learning (DFL) integrates predictive modeling and optimization by training predictors to optimize the downstream decision target rather than merely minimizing prediction error. To date, existing DFL methods typically rely on deterministic point predictions, which are often insufficient to capture the intrinsic stochasticity of real-world environments. To address this challenge, we propose the first diffusion-based DFL approach, which trains a diffusion model to represent the di…

On the Complexity of Stationary Nash Equilibria in Discounted Perfect Information Stochastic Games
Kristoffer Arnsfelt Hansen, Xinhao Nie
https://arxiv.org/abs/2510.11550 https:…

On the Complexity of Stationary Nash Equilibria in Discounted Perfect Information Stochastic Games
We study the problem of computing stationary Nash equilibria in discounted perfect information stochastic games from the viewpoint of computational complexity. For two-player games we prove the problem to be in PPAD, which together with a previous PPAD-hardness result precisely classifies the problem as PPAD-complete. In addition to this we give an improved and simpler PPAD-hardness proof for computing a stationary epsilon-Nash equilibrium. For 3-player games we construct games showing that rat…

General Decentralized Stochastic Optimal Control via Change of Measure: Applications to the Witsenhausen Counterexample
Bhagyashri Telsang, Seddik Djouadi, Charalambos D. Charalambous
https://arxiv.org/abs/2509.11013

General Decentralized Stochastic Optimal Control via Change of Measure: Applications to the Witsenhausen Counterexample
In this paper we present global and person-by-person (PbP) optimality conditions for general decentralized stochastic dynamic optimal control problems, using a discrete-time version of Girsanov's change of measure. The PbP optimality conditions are applied to the Witsenhausen counterexample to show that the two strategies satisfy two coupled nonlinear integral equations. Further, we prove a fixed point theorem in a function space, establishing existence and uniqueness of solutions to the integr…

Coherence of Supermassive Black Hole Binary Demographics with the nHz Stochastic Gravitational Wave Background
Katsunori Kusakabe, Yoshiyuki Inoue, Daisuke Toyouchi
https://arxiv.org/abs/2510.10548

Coherence of Supermassive Black Hole Binary Demographics with the nHz Stochastic Gravitational Wave Background
We present a refined estimation of the stochastic gravitational wave background (SGWB) based on observed dual active galactic nuclei (AGNs) together with AGN X-ray luminosity functions, in light of recent Pulsar Timing Array detections of an nHz SGWB. We identify a characteristic luminosity dependence in dual AGN fractions by compiling recent observational datasets, providing crucial constraints on supermassive black hole binary (SMBHB) populations. Our AGN-based model reproduces the current SG…

Transport properties of stochastic fluids
Chandrodoy Chattopadhyay, Josh Ott, Thomas Schaefer, Vladimir V. Skokov
https://arxiv.org/abs/2510.12557 https://…

Transport properties of stochastic fluids
We study heat conduction and momentum transport in the context of stochastic fluid dynamics. We consider a fluid described by model H in the classification of Hohenberg and Halperin. We study both non-critical and critical fluids, and we investigate transport properties in two as well as three dimensions. Our results are based on numerical simulations of model H using a Metropolis algorithm, and we employ Kubo relations to extract transport coefficients. We observe the expected logarithmic dive…

Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity
Partha Nandi, Partha Ghose, Francesco Petruccione
https://arxiv.org/abs/2510.10836 htt…

Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity
Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry but lack a natural mechanism for dynamical Dirac-type evolution, while the Wheeler--DeWitt equation typically enters only as an imposed constraint. We propose a stochastic framework in which each spin-network edge carries helicity-resolved amplitudes -- two-state internal labels that undergo Poisson-driven flips. The resulting coupled master equations, after analytic continuation and the introduction of a fu…

An inductive approach to stochastic estimates for the $\varphi^{4}_2$-equation with correlated coefficient field
Nicolas Clozeau
https://arxiv.org/abs/2509.11309 https://…

An inductive approach to stochastic estimates for the $φ^{4}_2$-equation with correlated coefficient field
We develop an inductive approach to obtaining stochastic estimates for the $φ^{4}_2$-equation when the coefficient field is correlated with the driving noise. Our method is based on (infinite-dimensional) Gaussian integration by parts with respect to Wick products of Gaussian random variables (more precisely, mollifications of space-time white noise)

Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximation
Bogdan Butyrin, Eric Moulines, Alexey Naumov, Sergey Samsonov, Qi-Man Shao, Zhuo-Song Zhang
https://arxiv.org/abs/2510.12375

Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximation
In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the normal approximation by the Gaussian distribution with covariance matrix predicted by the Polyak-Juditsky central limit theorem and establish the rate up to order $n^{-1/3}$ in convex distance, where $n$ is the number of samples used in the algorithm. We also prov…

Convective Space-Time Chaos as a Dynamical Model of Deterministic and Stochastic Turbulence
Arkady Pikovsky
https://arxiv.org/abs/2509.11341 https://arxiv.…

Convective Space-Time Chaos as a Dynamical Model of Deterministic and Stochastic Turbulence
Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. A deterministic property means that identical random perturbations at the inlet lead to identical patterns downstream; during this stage, the non-identical, stochastic component grows and eventually dominates the flow further downstream. We argue that these properties can be explained by exploring the concept of convective space-time chaos, where secondary perturbations…

Quantum deep reinforcement learning for humanoid robot navigation task
Romerik Lokossou, Birhanu Shimelis Girma, Ozan K. Tonguz, Ahmed Biyabani
https://arxiv.org/abs/2509.11388 …

Quantum deep reinforcement learning for humanoid robot navigation task
Classical reinforcement learning (RL) methods often struggle in complex, high-dimensional environments because of their extensive parameter requirements and challenges posed by stochastic, non-deterministic settings. This study introduces quantum deep reinforcement learning (QDRL) to train humanoid agents efficiently. While previous quantum RL models focused on smaller environments, such as wheeled robots and robotic arms, our work pioneers the application of QDRL to humanoid robotics, specific…

Rough stochastic filtering
Fabio Bugini, Peter K. Friz, Khoa L\^e, Huilin Zhang
https://arxiv.org/abs/2509.11825 https://arxiv.org/pdf/2509.11825

Rough stochastic filtering
The theory of rough stochastic differential equations (arXiv:2106.10340) is applied to revisit classical problems in stochastic filtering. We provide rough counterparts to the Kallianpur-Striebel formula and the Zakai and Kushner-Stratonovich equations, seen to coincide with classical objects upon randomization. We follow Crisan-Pardoux (arXiv:2411.11125) in doing so in a correlated diffusion setting. Well-posedness of the (rough) filtering equation is seen to hold under dimension-independent r…

Information-theoretic analysis of temporal dependence in discrete stochastic processes: Application to precipitation predictability
Juan De Gregorio, David S\'anchez, Ra\'ul Toral
https://arxiv.org/abs/2510.11276

Information-theoretic analysis of temporal dependence in discrete stochastic processes: Application to precipitation predictability
Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete stochastic processes and apply it to daily precipitation records across the contiguous United States. The method is based on the predictability gain, a quantity derived from block entropy that measures the additional information provided by higher-order temporal…

Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms
Anh Duc Nguyen, Alp Yurtsever, Suvrit Sra, Kim-Chuan Toh
https://arxiv.org/abs/2509.11657 https://…

Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms
In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the finite-sum setting, our method achieves a gradient computation complexity of $O(N + N^{1/2}\varepsilon^{-2})$ with sample size $N$, surpassing the previous best-known complexity of $O(N + N^{2/3}\varepsilon^{-2})$ for stochastic variance-reduced (SVR) DCA meth…

My latest essay, I will offiicially release it tomorrow morning, but in the meantime, here it is!
https://varnelis.net/works_and_projects/stochastic-histories/

Stochastic Histories - varnelis.net
stochastic histories /stəˈkæstɪk ˈhɪstəriz/ n. pl. [from Gk. stokhastikos “capable of guessing,” from stokhazesthai “to aim at, guess at” + L. historia “narrative, account”] 1. Fabricated historical narratives generated through iterative probabilistic sampling with artificial-intelligence systems, producing documentation that appears authentic through the accumulation of plausible details. 2. A mode of artistic practice that exploits ...

Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
Sami Raatikainen, Syksy Rasanen, Eemeli Tomberg
https://arxiv.org/abs/2510.09303

Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
We study stochastic effects in viable ultra-slow-roll inflation models that produce primordial black holes. We consider asteroid, solar, and supermassive black hole seed masses. In each case, we simulate $10^8$ patches of the universe that may collapse into PBHs. In every patch, we follow $4\times10^4$ momentum shells to construct its spherically symmetric profile from first principles, without introducing a window function. We include the effects of critical collapse and the radiation era tran…

On goodness-of-fit testing for volatility in McKean-Vlasov models
Akram Heidari, Mark Podolskij
https://arxiv.org/abs/2510.12607 https://arxiv.org/pdf/2510…

On goodness-of-fit testing for volatility in McKean-Vlasov models
This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics. While integrated volatility estimation in classical SDEs is now well established, formal model validation and goodness-of-fit testing for McKean-Vlasov systems remain largely unexplored, particularly in regimes with both large particle limits and high-frequen…

Stochastic Finite Volume Approximation with Clustering in the Parameter Space for Forward Uncertainty Quantification of PDEs with Random Parameters
Zhao Zhang, Na Ou
https://arxiv.org/abs/2510.12109

Stochastic Finite Volume Approximation with Clustering in the Parameter Space for Forward Uncertainty Quantification of PDEs with Random Parameters
The uncertainty quantification (UQ) for partial differential equations (PDEs) with random parameters is important for science and engineering. Forward UQ quantifies the impact of random parameters on the solution or the quantity-of-interest (QoI). In the current study, we propose a new extension of the stochastic finite volume (SFV) method by clustering samples in the parameter space. Compared to classic SFV based on structured grid in the parameter space, the new scheme based on clustering ext…

Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree
Aniss Aiman Medbouhi, Alejandro Garc\'ia-Castellanos, Giovanni Luca Marchetti, Daniel Pelt, Erik J Bekkers, Danica Kragic
https://arxiv.org/abs/2510.09328

Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree
We study the problem of constructing Steiner Minimal Trees (SMTs) in hyperbolic space. Exact SMT computation is NP-hard, and existing hyperbolic heuristics such as HyperSteiner are deterministic and often get trapped in locally suboptimal configurations. We introduce Randomized HyperSteiner (RHS), a stochastic Delaunay triangulation heuristic that incorporates randomness into the expansion process and refines candidate trees via Riemannian gradient descent optimization. Experiments on synthetic…

Energy Efficiency Maximization for Movable Antenna-Enhanced MIMO Downlink System Based on S-CSI
Xintai Chen, Biqian Feng, Yongpeng Wu, Xiang-Gen Xia, Chengshan Xiao
https://arxiv.org/abs/2509.12036

Energy Efficiency Maximization for Movable Antenna-Enhanced MIMO Downlink System Based on S-CSI
This paper presents an innovative movable antenna (MA)-enhanced multi-user multiple-input multiple-output (MIMO) downlink system. We aim to maximize the energy efficiency (EE) under statistical channel state information (S-CSI) through a joint optimization of the precoding matrix and the antenna position vectors (APVs). To solve the resulting stochastic problem, we first resort to deterministic equivalent (DE) tecnology to formulate the deterministic minorizing function of the system EE and the…

Resetting Induces Memory Loss in Non-Markovian Processes
Debasish Saha, Rati Sharma
https://arxiv.org/abs/2509.11608 https://arxiv.org/pdf/2509.11608

Resetting Induces Memory Loss in Non-Markovian Processes
Stochastic resetting is a powerful strategy known to accelerate the first-passage time statistics of stochastic processes. While its effects on Markovian systems are well understood, a general framework for non-Markovian dynamics is still lacking, mostly due to its mathematical complexity. Here, we present an analytical and numerical framework to study non-Markovian processes under resetting, focusing on the first-passage properties of escape kinetics from metastable states. We show that resett…

Complementarity of gravitational wave analyses and di-Higgs production in the exploration of the Electroweak Phase Transition dynamics in the RxSM
Johannes Braathen, Sven Heinemeyer, Carlos Pulido Boatella, Alain Verduras Schaeidt
https://arxiv.org/abs/2510.12569

Complementarity of gravitational wave analyses and di-Higgs production in the exploration of the Electroweak Phase Transition dynamics in the RxSM
The real singlet extension of the Standard Model (SM), RxSM, is one of the simplest Beyond-the-Standard Model (BSM) theories that can accommodate a strong first-order electroweak phase transition (SFOEWPT). We survey the possible thermal histories of the early Universe in the RxSM, and find that a SFOEWPT can occur in this model as single- or two-step phase transitions. We investigate complementary approaches to probe such scenarios experimentally: either via searches for a stochastic backgroun…

Crosslisted article(s) found for q-bio.NC. https://arxiv.org/list/q-bio.NC/new
[1/1]:
- Geometric Phase of Stochastic Oscillators
Yangyang Du
https://

About the Multiplicative Inverse of a Non-Zero-Mean Gaussian Process
Marco Lanucara
https://arxiv.org/abs/2509.11650 https://arxiv.org/pdf/2509.11650

About the Multiplicative Inverse of a Non-Zero-Mean Gaussian Process
We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a convergent series expansion of the autocorrelation function in powers of the ratio between mean and standard deviation of the underlying Gaussian process. We apply the results to two sample processes, and we validate the theoretical results with simulations based on s…

OSCAR: Orthogonal Stochastic Control for Alignment-Respecting Diversity in Flow Matching
Jingxuan Wu, Zhenglin Wan, Xingrui Yu, Yuzhe Yang, Bo An, Ivor Tsang
https://arxiv.org/abs/2510.09060

OSCAR: Orthogonal Stochastic Control for Alignment-Respecting Diversity in Flow Matching
Flow-based text-to-image models follow deterministic trajectories, forcing users to repeatedly sample to discover diverse modes, which is a costly and inefficient process. We present a training-free, inference-time control mechanism that makes the flow itself diversity-aware. Our method simultaneously encourages lateral spread among trajectories via a feature-space objective and reintroduces uncertainty through a time-scheduled stochastic perturbation. Crucially, this perturbation is projected …

Exosome-mediated chemotaxis optimizes leader-follower cell migration
Louis Gonz\'alez, Andrew Mugler
https://arxiv.org/abs/2510.11909 https://arxiv.org…

Exosome-mediated chemotaxis optimizes leader-follower cell migration
Cells frequently employ extracellular vesicles, or exosomes, to signal across long distances and coordinate collective actions. Exosomes diffuse slowly, can be actively degraded, and contain stochastic amounts of molecular cargo. These features raise the question of the efficacy of exosomes as a directional signal, but this question has not be systematically investigated. We develop a theoretical and computational approach to quantify the limits of exosome-mediated chemotaxis at the individual …

Travel Time and Weather-Aware Traffic Forecasting in a Conformal Graph Neural Network Framework
Mayur Patil, Qadeer Ahmed, Shawn Midlam-Mohler
https://arxiv.org/abs/2509.12043 h…

Travel Time and Weather-Aware Traffic Forecasting in a Conformal Graph Neural Network Framework
Traffic flow forecasting is essential for managing congestion, improving safety, and optimizing various transportation systems. However, it remains a prevailing challenge due to the stochastic nature of urban traffic and environmental factors. Better predictions require models capable of accommodating the traffic variability influenced by multiple dynamic and complex interdependent factors. In this work, we propose a Graph Neural Network (GNN) framework to address the stochasticity by leveragin…

Stochastic nonlinear wave equation with rougher than white noise
Xue-Mei Li, Xianfeng Ren
https://arxiv.org/abs/2510.12221 https://arxiv.org/pdf/2510.12221…

Stochastic nonlinear wave equation with rougher than white noise
We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Matérn forcing (a Fourier multiplier of order $α>0$ applied to space-time white noise) and establish local well-posedness for $α< \tfrac{3}{8}$. This extends [GKO18] beyond white noise and strengthens the quadratic-case result [OO21] ($α<\tfrac 12$). Our argument develops new trilinear estimates in Bourgain spaces together with sharp, case-specific cubic counting estimates.

Replaced article(s) found for physics.ed-ph. https://arxiv.org/list/physics.ed-ph/new
[1/1]:
- A stochastic approach in physics exercises of mathematics education
Matyas Barczy, Imre Kocsis, Csaba G\'abor K\'ezi

Replaced article(s) found for physics.chem-ph. https://arxiv.org/list/physics.chem-ph/new
[1/1]:
- Large Differences Between Stochastic and Deterministic Kinetics in a Simple Autocatalytic Reactio...
Tomasz Bednarek, Jakub J\k{e}drak

Crosslisted article(s) found for cond-mat.quant-gas. https://arxiv.org/list/cond-mat.quant-gas/new
[1/1]:
- Transport properties of stochastic fluids
Chandrodoy Chattopadhyay, Josh Ott, Thomas Schaefer, Vladimir V. Skokov

LIV-Decoherence on Gravitational Cat States
Iarley P. Lobo, Kelvin Sampaio, Gislaine Var\~ao, Moises Rojas, Valdir B. Bezerra
https://arxiv.org/abs/2510.08828 https://

LIV-Decoherence on Gravitational Cat States
Inspired by approaches based on the stochastic generalized uncertainty principle, we propose a Lindblad equation derived from the quantization of a stochastic modified dispersion relation in a Lorentz Invariance Violation (LIV) scenario. This framework enables us to investigate decoherence effects in a system of particles exhibiting gravitationally induced entanglement. We analyze the impact of LIV on entanglement (quantified by concurrence) considering systematic and stochastic effects.

Replaced article(s) found for q-fin.PR. https://arxiv.org/list/q-fin.PR/new
[1/1]:
- Short-maturity options on realized variance in local-stochastic volatility models
Dan Pirjol, Xiaoyu Wang, Lingjiong Zhu

Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control
Se Hwan Jeon, Ho Jae Lee, Seungwoo Hong, Sangbae Kim
https://arxiv.org/abs/2510.12717

Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control
Model Predictive Control (MPC) provides interpretable, tunable locomotion controllers grounded in physical models, but its robustness depends on frequent replanning and is limited by model mismatch and real-time computational constraints. Reinforcement Learning (RL), by contrast, can produce highly robust behaviors through stochastic training but often lacks interpretability, suffers from out-of-distribution failures, and requires intensive reward engineering. This work presents a GPU-paralleli…

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
Chuan He, Zhaosong Lu
https://arxiv.org/abs/2510.11676 https://a…

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs gradient clipping or normalization techniques in stochastic first-order methods to address heavy-tailed noise. In this paper, we demonstrate that a vanilla stochastic algorithm -- without additional modifications such as clipping or normalization -- can achieve op…

My artist's statement on my work with AI is out. I completely rethought what I am doing. This has been a worthwhile journey, for me, and I hope, for you if you read it.
https://varnelis.net/works_and_projects/stochastic-histories/

Stochastic Histories - varnelis.net
stochastic histories /stəˈkæstɪk ˈhɪstəriz/ n. pl. [from Gk. stokhastikos “capable of guessing,” from stokhazesthai “to aim at, guess at” + L. historia “narrative, account”] 1. Fabricated historical narratives generated through iterative probabilistic sampling with artificial-intelligence systems, producing documentation that appears authentic through the accumulation of plausible details. 2. A mode of artistic practice that exploits ...

Modeling Predator-Prey Dynamics with Stochastic Differential Equations: Patterns of Collective Hunting and Nonlinear Predation Effects
Junyi Qi, Ton Viet Ta
https://arxiv.org/abs/2510.08642

Modeling Predator-Prey Dynamics with Stochastic Differential Equations: Patterns of Collective Hunting and Nonlinear Predation Effects
We investigate predator-prey school interactions in aquatic environments using a stochastic differential equation (SDE)-based, particle-level model that incorporates attraction, repulsion, alignment, and environmental noise. Two predation strategies-center attack and nearest attack-are examined to assess their effects on prey survival, predator efficiency, and group dynamics. Simulations reveal diverse emergent behaviors such as prey dispersal and regrouping, oscillatory predation with collecti…

Ion Stochastic Heating by Low-frequency Alfv\'en Wave Spectrum
Jingyu Peng, Jiansen He
https://arxiv.org/abs/2510.07875 https://arxiv.org/pdf/2510.0787…

Ion Stochastic Heating by Low-frequency Alfvén Wave Spectrum
Finite-amplitude low-frequency Alfvén waves are commonly found in plasma environments, such as space plasmas, and play a crucial role in ion heating. The nonlinear interaction between oblique Alfvén wave spectra and ions has been studied. As the number of wave modes increases, ions are more likely to exhibit chaotic motion and experience stochastic heating. The stochastic heating threshold in the parameter space can be characterized by a single parameter, the effective relative curvature radi…

Stochastic numerical head phantoms to enable virtual imaging studies of transcranial photoacoustic computed tomography
Hsuan-Kai Huang, Joseph Kuo, Seonyeong Park, Umberto Villa, Lihong V. Wang, Mark A. Anastasio
https://arxiv.org/abs/2510.09758

Stochastic numerical head phantoms to enable virtual imaging studies of transcranial photoacoustic computed tomography
Transcranial photoacoustic computed tomography (PACT) is an emerging neuroimaging modality, but skull-induced aberrations can result in severe image artifacts if not compensated for during image reconstruction. The development of advanced image reconstruction methods for transcranial PACT is hindered by the lack of well-characterized, clinically relevant evaluation frameworks. Virtual imaging studies offer a solution, but require realistic numerical phantoms. To address this need, this study in…

Foraging with the Eyes: Dynamics in Human Visual Gaze and Deep Predictive Modeling
Tejaswi V. Panchagnula
https://arxiv.org/abs/2510.09299 https://arxiv.or…

Foraging with the Eyes: Dynamics in Human Visual Gaze and Deep Predictive Modeling
Animals often forage via Levy walks stochastic trajectories with heavy tailed step lengths optimized for sparse resource environments. We show that human visual gaze follows similar dynamics when scanning images. While traditional models emphasize image based saliency, the underlying spatiotemporal statistics of eye movements remain underexplored. Understanding these dynamics has broad applications in attention modeling and vision-based interfaces. In this study, we conducted a large scale huma…

Navier-Stokes Equations with Fractional Dissipation and Associated Doubly Stochastic Yule Cascades
Radu Dascaliuc, Tuan N. Pham, Enrique Thomann, Edward C. Waymire
https://arxiv.org/abs/2509.10806

Navier-Stokes Equations with Fractional Dissipation and Associated Doubly Stochastic Yule Cascades
Parametric regions are identified in terms of the spatial dimension $d$ and the power $γ$ of the Laplacian that separate explosive from non-explosive regimes for the self-similar doubly stochastic Yule cascades (DSY) naturally associated with the deterministic fractional Navier-Stokes equations (FNSE) on $\mathbb{R}^d$ in the scaling-supercritical setting. Explosion and/or geometric properties of the DSY, are then used to establish non-uniqueness, local existence, and finite-time blow-up resul…

Stochastic Homogenization of the Hamilton-Jacobi Equation on Manifolds
Marco Pozza, Alfonso Sorrentino
https://arxiv.org/abs/2510.11714 https://arxiv.org/p…

Stochastic Homogenization of the Hamilton-Jacobi Equation on Manifolds
This article establishes a stochastic homogenization result for the first order Hamilton-Jacobi equation on a Riemannian manifold $M$, in the context of a stationary ergodic random environment. The setting involves a finitely generated abelian group $ \mathtt{G}$ of rank $b$ acting on $M$ by isometries in a free, totally discontinuous, and co-compact manner, and a family of Hamiltonians $H: T^*M \times Ω\to \mathbb{R}$, parametrized over a probability space $(Ω, \mathbb{P})$, which are statio…

Evaluating the Quality of Randomness and Entropy in Tasks Supported by Large Language Models
Rabimba Karanjai, Yang Lu, Ranjith Chodavarapu, Lei Xu, Weidong Shi
https://arxiv.org/abs/2510.12080

Evaluating the Quality of Randomness and Entropy in Tasks Supported by Large Language Models
The rapid advancement of large language model (LLM) technology has led to diverse applications, many of which inherently require randomness, such as stochastic decision-making, gaming, scheduling, AI agents, and cryptography-related tasks. However, the capabilities of LLMs in handling randomness, particularly in generating and utilizing random numbers effectively, remain unclear. This paper investigates the capacity of LLMs for handling tasks that involve randomness through a series of experime…

Rate-Distortion Limits for Multimodal Retrieval: Theory, Optimal Codes, and Finite-Sample Guarantees
Thomas Y. Chen
https://arxiv.org/abs/2509.11054 https://

Rate-Distortion Limits for Multimodal Retrieval: Theory, Optimal Codes, and Finite-Sample Guarantees
We establish the first information-theoretic limits for multimodal retrieval. Casting ranking as lossy source coding, we derive a single-letter rate-distortion function $R(D)$ for reciprocal-rank distortion and prove a converse bound that splits into a modality-balanced term plus a skew penalty $κ\,ΔH$ capturing entropy imbalance and cross-modal redundancy. We then construct an explicit entropy-weighted stochastic quantizer with an adaptive, per-modality temperature decoder; a Blahut-Arimoto …

Nonanaliticities and ergodicity breaking in noninteracting many-body dynamics via stochastic resetting and global measurements
David Soldner, Igor Lesanovsky, Gabriele Perfetto
https://arxiv.org/abs/2510.11450

Nonanaliticities and ergodicity breaking in noninteracting many-body dynamics via stochastic resetting and global measurements
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially resolved measurement, the steady state can feature collective behavior similar to what is typically observed at phase transitions. Here we investigate such conditional reset protocol in a system of noninteracting spins, where the reset state is chosen as a ma…

Crosslisted article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- Edge-weighted Online Stochastic Matching: Beating $1-\frac1e$
Shuyi Yan
https://…

Optimizing Quantum Photonic Integrated Circuits using Differentiable Tensor Networks
Mathias Van Regemortel, Thomas Van Vaerenbergh
https://arxiv.org/abs/2509.11861 https://

Optimizing Quantum Photonic Integrated Circuits using Differentiable Tensor Networks
Recent reports of large photonic nonlinearities in integrated photonic devices, using the strong excitonic light-matter coupling in semiconductors, necessitate a tailored design framework for quantum processing in the limit of low photon occupation. We present a gradient-based optimization method for quantum photonic integrated circuits, which are composed of nonlinear unitary coupling gates and stochastic, nonunitary components for sampling the photonic losses. As core of our method, different…

S-D-RSM: Stochastic Distributed Regularized Splitting Method for Large-Scale Convex Optimization Problems
Maoran Wang, Xingju Cai, Yongxin Chen
https://arxiv.org/abs/2511.10133 https://arxiv.org/pdf/2511.10133 https://arxiv.org/html/2511.10133
arXiv:2511.10133v1 Announce Type: new
Abstract: This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks, compressed sensing, and so on. Stochastic gradient descent (SGD) and its variants are commonly employed to solve such problems. However, existing algorithms often rely on vanishing step sizes, strong convexity assumptions, or entail substantial computational overhead to ensure convergence or obtain favorable complexity. To bridge the gap between theory and practice, we integrate consensus optimization and operator splitting techniques (see Problem Reformulation) to develop a novel stochastic splitting algorithm, termed the \emph{stochastic distributed regularized splitting method} (S-D-RSM). In practice, S-D-RSM performs parallel updates of proximal mappings and gradient information for only a randomly selected subset of agents at each iteration. By introducing regularization terms, it effectively mitigates consensus discrepancies among distributed nodes. In contrast to conventional stochastic methods, our theoretical analysis establishes that S-D-RSM achieves global convergence without requiring diminishing step sizes or strong convexity assumptions. Furthermore, it achieves an iteration complexity of $\mathcal{O}(1/\epsilon)$ with respect to both the objective function value and the consensus error. Numerical experiments show that S-D-RSM achieves up to 2--3$\times$ speedup compared to state-of-the-art baselines, while maintaining comparable or better accuracy. These results not only validate the algorithm's theoretical guarantees but also demonstrate its effectiveness in practical tasks such as compressed sensing and empirical risk minimization.
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Rank Aggregation under Weak Stochastic Transitivity via a Maximum Score Estimator
Haoran Zhang, Yunxiao Chen
https://arxiv.org/abs/2510.06789 https://arxiv…

Rank Aggregation under Weak Stochastic Transitivity via a Maximum Score Estimator
Stochastic transitivity is central for rank aggregation based on pairwise comparison data. The existing models, including the Thurstone, Bradley-Terry (BT), and nonparametric BT models, adopt a strong notion of stochastic transitivity, known as strong stochastic transitivity (SST). This assumption imposes restrictive monotonicity constraints on the pairwise comparison probabilities, which is often unrealistic for real-world applications. This paper introduces a maximum score estimator for aggre…

Crosslisted article(s) found for math.ST. https://arxiv.org/list/math.ST/new
[1/1]:
- Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
Jia-Qi Yang, Lei Shi

Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs
Qi Yan, Xiang-Dong Li
https://arxiv.org/abs/2510.09383 https://ar…

Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs
We are concerned with a stochastic mean curvature flow of graphs with extra force over a periodic domain of any dimension. Based on compact embedding method of variational SPDE, we prove the existence of martingale solution. Moreover, we derive the small perturbation limit of the stochastic weighted mean curvature flow.

Stochastic and deterministic reaction-diffusion equations
Davide A. Bignamini, Paolo De Fazio
https://arxiv.org/abs/2510.10842 https://arxiv.org/pdf/2510.1…

Stochastic and deterministic reaction-diffusion equations
In this paper, we prove the well-posedness of non-autonomous deterministc and stochatic reaction-diffiusion equations. Concerning the stochastic problem, we prove also a result on the space-time regularity of the non-autonomous stochastic convoltution.

Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics
Joanna Marks, Tim Y. J. Wang, O. Deniz Akyildiz
https://arxiv.org/abs/2510.12311 https://

Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics
We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and pro…

Privacy-Preserving Uncertainty Disclosure for Facilitating Enhanced Energy Storage Dispatch
Ning Qi, Xiaolong Jin, Kai Hou, Zeyu Liu, Hongjie Jia, Wei Wei
https://arxiv.org/abs/2509.11022

Privacy-Preserving Uncertainty Disclosure for Facilitating Enhanced Energy Storage Dispatch
This paper proposes a novel privacy-preserving uncertainty disclosure framework, enabling system operators to release marginal value function bounds to reduce the conservativeness of interval forecast and mitigate excessive withholding, thereby enhancing storage dispatch and social welfare. We propose a risk-averse analytical storage arbitrage model based on stochastic dynamic programming and explicitly account for uncertainty intervals in value function training. We derive real-time marginal v…

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
Nicholas Pischke
https://arxiv.org/abs/2510.10697 https://

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence under a suitable strong monotonicity assumption, together with a probabilistic independence assumption and a separability assumption on the tangent spaces. As a particular case, our results transfer previous work by P. Bianchi on that method in Hilbert space…

Modeling, Segmenting and Statistics of Transient Spindles via Two-Dimensional Ornstein-Uhlenbeck Dynamics
C. Sun, D. Fettahoglu, D. Holcman
https://arxiv.org/abs/2512.10844 https://arxiv.org/pdf/2512.10844 https://arxiv.org/html/2512.10844
arXiv:2512.10844v1 Announce Type: new
Abstract: We develop here a stochastic framework for modeling and segmenting transient spindle- like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individ- ual spindles are represented as path realizations of a two-dimensional Ornstein{Uhlenbeck (OU) process with a stable focus, providing a low-dimensional stochastic dynamical sys- tem whose trajectories reproduce key morphological features of spindles, including their characteristic rise{decay amplitude envelopes. On the signal processing side, we propose a segmentation procedure based on Empirical Mode Decomposition (EMD) combined with the detection of a central extremum, which isolates single spindle events and yields a collection of oscillatory atoms. This construction enables a systematic statistical analysis of spindle features: we derive empirical laws for the distributions of amplitudes, inter-spindle intervals, and rise/decay durations, and show that these exhibit exponential tails consistent with the underlying OU dynamics. We further extend the model to a pair of weakly coupled OU processes with distinct natural frequencies, generating a stochastic mixture of slow, fast, and mixed spindles in random temporal order. The resulting framework provides a data- driven framework for the analysis of transient oscillations in EEG and, more generally, in nonstationary time series.
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Bistability and Noise-Induced Evasion in Tumor-Immune Dynamics with Antigen Accumulation and Immune Escape
Mengfan Tan, Shaoqing Chen, Chunjin Wei, Da Zhou
https://arxiv.org/abs/2509.11048

Bistability and Noise-Induced Evasion in Tumor-Immune Dynamics with Antigen Accumulation and Immune Escape
Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a four-compartment dynamical model that incorporates antigen accumulation and immune escape mutations. Bifurcation analysis reveals bistability between immune surveillance and immune escape states, providing a mechanistic explanation for heterogeneous immune outcom…

An Eulerian Perspective on Straight-Line Sampling
Panos Tsimpos, Youssef Marzouk
https://arxiv.org/abs/2510.11657 https://arxiv.org/pdf/2510.11657

An Eulerian Perspective on Straight-Line Sampling
We study dynamic measure transport for generative modeling: specifically, flows induced by stochastic processes that bridge a specified source and target distribution. The conditional expectation of the process' velocity defines an ODE whose flow map achieves the desired transport. We ask \emph{which processes produce straight-line flows} -- i.e., flows whose pointwise acceleration vanishes and thus are exactly integrable with a first-order method? We provide a concise PDE characterization of s…

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[2/2]:
- A geometric formulation of GENERIC stochastic differential equations
Mark A. Peletier, Marcello Seri
…

Monte Carlo quasi-interpolation of spherical data
Zhengjie Sun, Mengyuan Lv, Xingping Sun
https://arxiv.org/abs/2510.12027 https://arxiv.org/pdf/2510.12027…

Monte Carlo quasi-interpolation of spherical data
We establish a deterministic and stochastic spherical quasi-interpolation framework featuring scaled zonal kernels derived from radial basis functions on the ambient Euclidean space. The method incorporates both quasi-Monte Carlo and Monte Carlo quadrature rules to construct easily computable quasi-interpolants, which provide efficient approximation to Sobolev-space functions for both clean and noisy data. To enhance the approximation power and robustness of our quasi-interpolants, we develop a…

On the negativity of the top Lyapunov exponent for stochastic differential equations driven by fractional Brownian motion
Alexandra Blessing Neam\c{t}u, Mazyar Ghani Varzaneh
https://arxiv.org/abs/2510.11531

On the negativity of the top Lyapunov exponent for stochastic differential equations driven by fractional Brownian motion
We provide sign information for the top Lyapunov exponent for a stochastic differential equation driven by fractional Brownian motion.~To this aim we analyze the stochastic dynamical system generated by such an equation, obtain a random dynamical system and construct an appropriate invariant measure.~Suitable estimates for its density together with Birkhoff's ergodic theorem imply the negativity of the top Lyapunov exponent by increasing the noise intensity.

Martingale Optimal Transport and Martingale Schr\"odinger Bridges for Calibration of Stochastic Volatility Models
Antonios Zitridis
https://arxiv.org/abs/2510.10860 https:/…

Martingale Optimal Transport and Martingale Schrödinger Bridges for Calibration of Stochastic Volatility Models
Motivated by recent developments in the calibration of stochastic volatility models (SVMs for short), we study continuous-time formulations of martingale optimal transport and martingale Schrödinger bridge problems. We establish duality formulas and also provide alternative proofs, via different techniques, of duality results previously established in the mathematical finance literature. Applications include calibration of SVMs to SPX options, as well as joint calibration to both SPX and VIX o…

Universal behaviors of the multi-time correlation functions of random processes with renewal: the step noise case (the random velocity of a L\'evy walk)
Marco Bianucci, Mauro Bologna, Daniele Lagomarsino-Oneto, Riccardo Mannella
https://arxiv.org/abs/2510.11747

Universal behaviors of the multi-time correlation functions of random processes with renewal: the step noise case (the random velocity of a Lévy walk)
Stochastic processes with renewal properties are powerful tools for modeling systems where memory effects and long-time correlations play a significant role. In this work, we study a broad class of renewal processes where a variable's value changes according to a prescribed Probability Density Function (PDF), $p(ξ)$, after random waiting times $θ$. This model is relevant across many fields, including classical chaos, nonlinear hydrodynamics, quantum dots, cold atom dynamics, biological motion…

Analysis and Design of Spare Strategy for Large-Scale Satellite Constellation Using Direct Insertion under (r,q) Policy
Seungyeop Han, Zachary Grieser, Shoji Yoshikawa, Takumi Noro, Takumi Suda, Koki Ho
https://arxiv.org/abs/2509.10585

Analysis and Design of Spare Strategy for Large-Scale Satellite Constellation Using Direct Insertion under (r,q) Policy
This paper introduces a Markov chain-based approach for the analysis and optimization of spare-management policies in large-scale satellite constellations. Focusing on the direct strategy, we model spare replenishment as a periodic-review reorder-point/order-quantity policy, where spares are deployed directly to constellation planes. The stochastic behavior of satellite failures and launch vehicle lead times is captured through Markov representations of both failure and replenishment dynamics. …

Optimizing optimal transport: Role of final distributions in finite-time thermodynamics
Kaito Tojo, Rihito Nagase, Ken Funo, Takahiro Sagawa
https://arxiv.org/abs/2509.11314 htt…

Optimizing optimal transport: Role of final distributions in finite-time thermodynamics
Performing thermodynamic tasks within finite time while minimizing thermodynamic costs is a central challenge in stochastic thermodynamics. Here, we develop a unified framework for optimizing the thermodynamic cost of performing various tasks in finite time for overdamped Langevin systems. Conventional optimization of thermodynamic cost based on optimal transport theory leaves room for varying the final distributions according to the intended task, enabling further optimization. Taking advantag…

Empowering Prosumers: Incentive Design for Local Electricity Markets Under Generalized Uncertainty and Grid Constraints
P{\aa}l Forr Austnes, Matthieu Jacobs, Lu Wang, Mario Paolone
https://arxiv.org/abs/2510.12318

Empowering Prosumers: Incentive Design for Local Electricity Markets Under Generalized Uncertainty and Grid Constraints
Since the 1990s, widespread introduction of central (wholesale) electricity markets has been seen across multiple continents, driven by the search for efficient operation of the power grid through competition. The increase of renewables has made significant impacts both on central electricity markets and distribution-level grids as renewable power generation is often connected to the latter. These stochastic renewable technologies have both advantages and disadvantages. On one hand they offer v…

Flatness-Aware Stochastic Gradient Langevin Dynamics
Stefano Bruno, Youngsik Hwang, Jaehyeon An, Sotirios Sabanis, Dong-Young Lim
https://arxiv.org/abs/2510.02174 https://

Flatness-Aware Stochastic Gradient Langevin Dynamics
Generalization in deep learning is closely tied to the pursuit of flat minima in the loss landscape, yet classical Stochastic Gradient Langevin Dynamics (SGLD) offers no mechanism to bias its dynamics toward such low-curvature solutions. This work introduces Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD), designed to efficiently and provably seek flat minima in high-dimensional nonconvex optimization problems. At each iteration, fSGLD uses the stochastic gradient evaluated at para…

Nonlinearly Preconditioned Gradient Methods: Momentum and Stochastic Analysis
Konstantinos Oikonomidis, Jan Quan, Panagiotis Patrinos
https://arxiv.org/abs/2510.11312 https://…

Nonlinearly Preconditioned Gradient Methods: Momentum and Stochastic Analysis
We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique. Building upon this idea, we introduce a novel heavy ball-type algorithm and provide convergence guarantees under a generalized smoothness condition that is less restrictive than traditional Lipschitz smoothness, thus covering a broader class of functions. Addit…

Stochastic BDDC algorithms
Xuemin Tu, Jinjin Zhang
https://arxiv.org/abs/2510.05993 https://arxiv.org/pdf/2510.05993

Stochastic BDDC algorithms
Stochastic balancing domain decomposition by constraints (BDDC) algorithms are developed and analyzed for the sampling of the solutions of linear stochastic elliptic equations with random coefficients. Different from the deterministic BDDC algorithms, the stochastic BDDC algorithms have online and offline stages. At the offline stage, the Polynomial Chaos (PC) expansions of different components of the BDDC algorithms are constructed based on the subdomain local parametrization of the stochastic…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[2/2]:
- Distance Between Stochastic Linear Systems
Venkatraman Renganathan, Sei Zhen Khong

Post-hoc Stochastic Concept Bottleneck Models
Wiktor Jan Hoffmann, Sonia Laguna, Moritz Vandenhirtz, Emanuele Palumbo, Julia E. Vogt
https://arxiv.org/abs/2510.08219 https://

Post-hoc Stochastic Concept Bottleneck Models
Concept Bottleneck Models (CBMs) are interpretable models that predict the target variable through high-level human-understandable concepts, allowing users to intervene on mispredicted concepts to adjust the final output. While recent work has shown that modeling dependencies between concepts can improve CBM performance, especially under interventions, such approaches typically require retraining the entire model, which may be infeasible when access to the original data or compute is limited. I…

On the approximation of finite-time Lyapunov exponents for the stochastic Burgers equation
Alexandra Blessing, Dirk Bl\"omker
https://arxiv.org/abs/2510.09460 https://

On the approximation of finite-time Lyapunov exponents for the stochastic Burgers equation
We analyze stochastic partial differential equations (SPDEs) with quadratic nonlinearities close to a change of stability. To this aim we compute finite-time Lyapunov exponents (FTLEs), observing a change of sign based on the interplay between the distance towards the bifurcation and the noise intensity. A technical challenge is to provide a suitable control of the nonlinear terms coupling the dominant and stable modes of the SPDE and of the corresponding linearization. In order to illustrate o…

Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization
Xiaobing Feng, Liet Vo
https://arxiv.org/abs/2510.08291

Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization
This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative noise. Additionally, it introduces a novel approach and framework for the numerical analysis of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noise in general. The main ideas of this approach include establishing exponential s…

A unified optimal control framework: time-optimal control and stochastic optimal control
Shuzhen Yang
https://arxiv.org/abs/2510.07765 https://arxiv.org/pd…

A unified optimal control framework: time-optimal control and stochastic optimal control
In this paper, we propose a unified stochastic optimal control framework that bridges time-optimal control problems and classical stochastic optimal control problems. Unlike traditional deterministic time-optimal control formulations, our framework incorporates a generalized stochastic control structure under minimum-time constraints. Here, the minimum-time condition characterizes the earliest achievable moment for reaching a target state in expectation, rendering the terminal time an endogenou…

Rethinking Langevin Thompson Sampling from A Stochastic Approximation Perspective
Weixin Wang, Haoyang Zheng, Guang Lin, Wei Deng, Pan Xu
https://arxiv.org/abs/2510.05023 https:…

Rethinking Langevin Thompson Sampling from A Stochastic Approximation Perspective
Most existing approximate Thompson Sampling (TS) algorithms for multi-armed bandits use Stochastic Gradient Langevin Dynamics (SGLD) or its variants in each round to sample from the posterior, relaxing the need for conjugacy assumptions between priors and reward distributions in vanilla TS. However, they often require approximating a different posterior distribution in different round of the bandit problem. This requires tricky, round-specific tuning of hyperparameters such as dynamic learning …

Brownian motion on the Fubini extension space and applications
Hamed Amini, Nina H. Amini, Sofiane Chalal, Gaoyue Guo
https://arxiv.org/abs/2509.12096 https://

Brownian motion on the Fubini extension space and applications
The aim of this paper is to establish a certain equivalence between a Brownian motion on a Fubini extension space and a collection of essentially pairwise independent Brownian motions on the marginal sample spaces. This equivalence allows us to state a Girsanov theorem that preserves pairwise independence and to formulate graphon stochastic differential equations as a single McKean-Vlasov type equation driven by a standard Brownian motion.

Bandits with Single-Peaked Preferences and Limited Resources
Gur Keinan, Rotem Torkan, Omer Ben-Porat
https://arxiv.org/abs/2510.09425 https://arxiv.org/pd…

Bandits with Single-Peaked Preferences and Limited Resources
We study an online stochastic matching problem in which an algorithm sequentially matches $U$ users to $K$ arms, aiming to maximize cumulative reward over $T$ rounds under budget constraints. Without structural assumptions, computing the optimal matching is NP-hard, making online learning computationally infeasible. To overcome this barrier, we focus on \emph{single-peaked preferences} -- a well-established structure in social choice theory, where users' preferences are unimodal with respect to…

New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process
Dmitriy F. Kuznetsov
https://arxiv.org/abs/2510.06981

New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process
The article is devoted to the systematic derivation of new representations of the Hu-Meyer formulas. The formula expressing a multiple Wiener stochastic integral through the sum of multiple Stratonovich stochastic integrals and the formula expressing a multiple Stratonovich stochastic integral through the sum of multiple Wiener stochastic integrals are derived for the case of a multidimensional Wiener process. The proof method proposed by the author in 2006 is applied. At that a different defin…

Re$^3$MCN: Cubic Newton Variance Reduction Momentum Quadratic Regularization for Finite-sum Non-convex Problems
Dmitry Pasechnyuk-Vilensky, Dmitry Kamzolov, Martin Tak\'a\v{c}
https://arxiv.org/abs/2510.08714

Re$^3$MCN: Cubic Newton + Variance Reduction + Momentum + Quadratic Regularization for Finite-sum Non-convex Problems
We analyze a stochastic cubic regularized Newton method for finite sum optimization $\textstyle\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$, that uses SARAH-type recursive variance reduction with mini-batches of size $b\sim n^{1/2}$ and exponential moving averages (EMA) for gradient and Hessian estimators. We show that the method achieves a $(\varepsilon,\sqrt{L_2\varepsilon})$-second-order stationary point (SOSP) with total stochastic oracle calls $n + \widetilde{\mathcal…

Grid Restoration Under Uncertainty Considering Coupled Transportation-Power Networks
Harshal D. Kaushik, Roshni Anna Jacob, Souma Chowdhury, Jie Zhang
https://arxiv.org/abs/2510.10399

Grid Restoration Under Uncertainty Considering Coupled Transportation-Power Networks
A stochastic mixed-integer programming model is developed to address the power distribution system repair and restoration following failures caused by extreme events such as natural disasters. This model addresses the complex challenge of efficiently assigning and dispatching repair crews to minimize both downtime and the extent of outages, following the crew sequence constraints. By incorporating a realistic transportation network, our model accounts for uncertainties in repair times, repair d…

Well-posedness of McKean-Vlasov generalized multivalued BSDEs
Qi Liu
https://arxiv.org/abs/2510.10026 https://arxiv.org/pdf/2510.10026

Well-posedness of McKean-Vlasov generalized multivalued BSDEs
This paper investigates McKean-Vlasov backward stochastic variational inequalities (BSVIs) whose generator depends on the joint law of the solution. We first establish the existence and uniqueness of the solution under globally Lipschitz and linear growth conditions. The analysis is then extended to the more general case of locally Lipschitz and non-linear growth conditions.

Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning
Jingyi Wu, Chao Ning, Yang Shi
https://arxiv.org/abs/2510.10214 https://

Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning
Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before sequentially incorporating them into downstream control synthesis. This segregation between ambiguity set construction and control objectives inherently introduces a structural misalignment, which undesirably leads to conservative control policies with sub-opt…

Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limits
Abdurakhmon Sadiev, Peter Richt\'arik, Ilyas Fatkhullin
https://arxiv.org/abs/2510.10690

Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limits
Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in light-tailed or bounded-noise settings, such algorithms are often brittle and lack guarantees under heavy-tailed noise -- precisely the regimes where robustness is most critical. In this work, we take a first step toward a theoretical understanding of second-order opt…