Tootfinder

Explainable Learning Rate Regimes for Stochastic Optimization
Zhuang Yang
https://arxiv.org/abs/2508.13639 https://arxiv.org/pdf/2508.13639

Explainable Learning Rate Regimes for Stochastic Optimization
Modern machine learning is trained by stochastic gradient descent (SGD), whose performance critically depends on how the learning rate (LR) is adjusted and decreased over time. Yet existing LR regimes may be intricate, or need to tune one or more additional hyper-parameters manually whose bottlenecks include huge computational expenditure, time and power in practice. This work, in a natural and direct manner, clarifies how LR should be updated automatically only according to the intrinsic varia…

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Guillaume Garrigos, Daniel Cortild, Lucas Ketels, Juan Peypouquet
https://arxiv.org/abs/2507.14122

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate of SGD in this context. Recent advances suggest that it should be possible. For instance, it can be achieved by making the additional, yet unverifiable, assumption that the variance of the stochastic gradients is uniformly bounded. In this paper, we show that …

Analytical phase boundary of a quantum driven-dissipative Kerr oscillator from classical stochastic instantons
Th\'eo S\'epulcre
https://arxiv.org/abs/2508.13925 https:/…

Analytical phase boundary of a quantum driven-dissipative Kerr oscillator from classical stochastic instantons
The framework of Keldysh path integral concisely describes quantum systems driven away from thermal equilibrium, such as the two-photon driven Kerr oscillator. Within the thermodynamic limit of diverging photon occupation, we map it to a Martin-Siggia-Rose-Janssen-de Dominicis path integral, and obtain a purely classical, stochastic equivalent where photon self-interaction plays the role of temperature. This perspective sheds light on the difficulties encountered in the search for an effective …

Pricing Options on Forwards in Function-Valued Affine Stochastic Volatility Models
Jian He, Sven Karbach, Asma Khedher
https://arxiv.org/abs/2508.14813 https://

Pricing Options on Forwards in Function-Valued Affine Stochastic Volatility Models
We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the Heath-Jarrow-Morton-Musiela framework as solution to a stochastic partial differential equation modulated by a stochastic volatility process. We analyze two classes of affine stochastic volatility models: (i) a Gaussian model governed by a finite-rank Wishart process…

Propagation of Singularities for the Damped Stochastic Klein-Gordon Equation
Hongyi Chen, Cheuk Yin Lee
https://arxiv.org/abs/2508.13671 https://arxiv.org/…

Propagation of Singularities for the Damped Stochastic Klein-Gordon Equation
For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides evidence for possible connections to microlocal analysis, ie. the exact regularity and singularities described in this paper should admit wavefront set type descriptions whose propagation is determined by the highest order terms of the linear operator. Despite the …

Stochastic Black Start Resource Allocation to Enable Dynamic Formation of Networked Microgrids and DER-aided Restoration
Cong Bai, Salish Maharjan, Han Wang, Zhaoyu Wang
https://arxiv.org/abs/2508.13306

Stochastic Black Start Resource Allocation to Enable Dynamic Formation of Networked Microgrids and DER-aided Restoration
Extended outages in distributed systems (DSs) dominated by distributed energy resources (DERs) require innovative strategies to efficiently and securely deploy black start (BS) resources. To address the need, this paper proposes a two-stage stochastic resource allocation method within synchronizing dynamic microgrids (MGs) for black start (SDMG-BS), enabling risk-averse and adaptive restoration across various scenarios while ensuring frequency security. Virtual synchronous generator (VSG)-contr…

Stochastic synaptic dynamics under learning
Jakob Stubenrauch, Naomi Auer, Richard Kempter, Benjamin Lindner
https://arxiv.org/abs/2508.13846 https://arxiv…

Stochastic synaptic dynamics under learning
Learning is based on synaptic plasticity, which drives and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic framework to capture the noisy synaptic dynamics. We consider a paradigmatic supervised learning example: a presynaptic neural population impinging in a sequence of episodes on a recurrent network of integrate-and-fire neurons through synapses undergoing spike-t…

Strong solutions for a class of stochastic thermo-magneto-hydrodynamic-type systems with multiplicative noise
Agus L. Soenjaya, Thanh Tran
https://arxiv.org/abs/2509.14490 https…

Strong solutions for a class of stochastic thermo-magneto-hydrodynamic-type systems with multiplicative noise
We study the existence and uniqueness of strong solutions, in the sense of PDEs and probability, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$ ($d\leq 3$), perturbed by spatially correlated multiplicative noise. Our framework applies to many physically relevant systems, including stochastic convective Brinkman--Forchheimer equations, stochastic magnetohydrodynamics (MHD), stochastic Bénard convection in po…

Convergent Reinforcement Learning Algorithms for Stochastic Shortest Path Problem
Soumyajit Guin, Shalabh Bhatnagar
https://arxiv.org/abs/2508.13963 https://

Convergent Reinforcement Learning Algorithms for Stochastic Shortest Path Problem
In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algo…

Cost Reduction in Spin-dependent Stochastic GW Calculations
Xuance Jiang, Vojtech Vlcek
https://arxiv.org/abs/2509.14700 https://arxiv.org/pdf/2509.14700…

Cost Reduction in Spin-dependent Stochastic GW Calculations
We extend the stochastic GW (sGW) formalism to fully spin-polarized systems, encompassing both collinear and non-collinear spin configurations. For non-collinear systems-where Kohn-Sham states are complex two-component spinors-we develop a complex-valued stochastic basis that preserves the real-valued external stochastic charge applied at time zero. This basis enables an unbiased evaluation of the random-phase approximation (RPA) screened interaction for spinors. Through error analysis and test…

Stochastic urban planning for housing: Reduce regulations with no provision to provide housing supporting the mix of incomes in California.
After all, in our system, return on capital plays no role in determining what price developers demand for building./s
https://www.s…

Stochastic urban planning for housing: Reduce regulations with no provision to provide housing supporting the mix of incomes in California.
After all, in our system, return on capital plays no role in determining what price developers demand for building./s
https://www.s…

Strongly correlated stochastic systems
Marco Biroli
https://arxiv.org/abs/2508.12818 https://arxiv.org/pdf/2508.12818…

Strongly correlated stochastic systems
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the universal characterization of conditionally independent identically distributed variables-random variables that become independent upon conditioning on latent parameters. This structure arises naturally in systems with stochastic resetting, a mechanism that ge…

Generative Super-Resolution of Turbulent Flows via Stochastic Interpolants
Martin Schi{\o}dt, Nikolaj Takata M\"ucke, Clara Marika Velte
https://arxiv.org/abs/2508.13770 ht…

Generative Super-Resolution of Turbulent Flows via Stochastic Interpolants
Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only coarse representations of the flows are feasible, leaving crucial fine-scale dynamics unresolved. This study addresses that limitation by leveraging generative models to perform super-resolution of velocity fields and reconstruct the unresolved scales from low-re…

Online Stochastic Packing with General Correlations
Sabri Cetin, Yilun Chen, David A. Goldberg
https://arxiv.org/abs/2508.13458 https://arxiv.org/pdf/2508.…

Online Stochastic Packing with General Correlations
There has been a growing interest in studying online stochastic packing under more general correlation structures, motivated by the complex data sets and models driving modern applications. Several past works either assume correlations are weak or have a particular structure, have a complexity scaling with the number of Markovian "states of the world" (which may be exponentially large e.g. in the case of full history dependence), scale poorly with the horizon $T$, or make additional continuity …

Importance of Shot Noise in the Search for an Isotropic Stochastic Gravitational-Wave Background with Next Generation Detectors
Haowen Zhong, Vuk Mandic
https://arxiv.org/abs/2509.15014

Importance of Shot Noise in the Search for an Isotropic Stochastic Gravitational-Wave Background with Next Generation Detectors
We investigate the impact of shot noise on the stochastic gravitational wave background generated by binary neutron star mergers, and confirm that the overall background can be significantly influenced by relatively few neighboring, loud events. To mitigate the shot noise, we propose a procedure to remove nearby events by notching them out in the time-frequency domain. Additionally, we quantify the cosmic/sample variance of the resulting background after notching, and we study the deviation bet…

Linking Stochastic Self-Propagating Star Formation and Spatio-Temporal Point Processes
Qihan Zou
https://arxiv.org/abs/2508.12372 https://arxiv.org/pdf/250…

Linking Stochastic Self-Propagating Star Formation and Spatio-Temporal Point Processes
The stochastic self-propagating star-formation (SSPSF) model is an important theoretical framework for explaining how localised star-formation events trigger subsequent activity across galactic discs. While widely used to interpret spiral and irregular structures, its probabilistic rules have lacked a formal statistical foundation. In this work, we establish a connection between the SSPSF model and spatio-temporal point processes (STPP), which describe events in space and time through history-d…

Nonparametric learning of stochastic differential equations from sparse and noisy data
Arnab Ganguly, Riten Mitra, Jinpu Zhou
https://arxiv.org/abs/2508.11597 https://

Nonparametric learning of stochastic differential equations from sparse and noisy data
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift, our goal here is to learn the entire drift function directly from data without strong structural assumptions, making it especially relevant in scientific disciplines where system dynamics are partially understood or highly complex. We cast the estimation prob…

Steering chiral active Brownian motion via stochastic position-orientation resetting
Amir Shee
https://arxiv.org/abs/2508.12223 https://arxiv.org/pdf/2508.…

Steering chiral active Brownian motion via stochastic position-orientation resetting
Guiding active motion is important for targeted delivery, sensing, and search tasks. Many active systems exhibit circular swimming, ubiquitous in chemical, physical, and biological systems, that biases motion and reduces transport efficiency. We show that stochastic position-orientation resetting can overcome these limitations in two-dimensional chiral active Brownian particles by interrupting circular motion, resulting in tunable dynamics. When resets are infrequent compared to chiral rotation…

$\alpha$-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed L\'evy noise beyond Lipschitz continuity
Jingwei Chen
https://arxiv.org/abs/2508.12909

$α$-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity
This paper develops an $α$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs) with time-space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly w…

Nonlinear stochastic trajectory optimization
Thomas Caleb, Roberto Armellin, St\'ephanie Lizy-Destrez
https://arxiv.org/abs/2508.13677 https://arxiv.or…

Nonlinear stochastic trajectory optimization
Designing robust space trajectories in nonlinear dynamical environments, such as the Earth-Moon circular restricted three-body problem (CR3BP), poses significant challenges due to sensitivity to initial conditions and non-Gaussian uncertainty propagation. This work introduces a novel solver for discrete-time chance-constrained trajectory optimization under uncertainty, referred to as stochastic optimization with differential algebra (SODA). SODA combines differential algebra (DA) with adaptive …

Random attractor and SRB measure for stochastic Hopf bifurcation under discretization
Chuchu Chen, Jialin Hong, Yibo Wang
https://arxiv.org/abs/2509.12865 https://

Random attractor and SRB measure for stochastic Hopf bifurcation under discretization
Chaotic phases in stochastic differential equations are characterized by two essential long-time dynamical features: a random attractor capturing asymptotic geometry and a Sinai-Ruelle-Bowen (SRB) measure describing statistical information. This paper investigates whether the stochastic Hopf bifurcation under discretization could inherit both features. We establish that the stochastic Hopf bifurcation under discretization induces a discrete random dynamical system. Further, we prove that this d…

The Stochastic Dissipation Model for the Steady State Neutrino and Multi-Wavelength Emission of TXS 0506 056
Zhen-Jie Wang, Ruo-Yu Liu, Xiang-Yu Wang
https://arxiv.org/abs/2509.14587

The Stochastic Dissipation Model for the Steady State Neutrino and Multi-Wavelength Emission of TXS 0506+056
The blazar TXS 0506+056 has been suggested to be a potential high-energy neutrino source thanks to the observations of IceCube, which found outburst-like neutrino emissions during 2014-2015 and 2017 in the transient emission search, and a $3.5σ$ local significance in a 10-year time-integrated search. The conventional one-zone jet model cannot explain the observed neutrino flux during outbursts due to the constraint from the X-ray flux, leading to proposals of multi-zone models (e.g. two-zone m…

Sound Value Iteration for Simple Stochastic Games
Muqsit Azeem (Technical University of Munich), Jan Kretinsky (Masaryk University), Maximilian Weininger (Ruhr-University Bochum)
https://arxiv.org/abs/2509.14112

Sound Value Iteration for Simple Stochastic Games
Algorithmic analysis of Markov decision processes (MDP) and stochastic games (SG) in practice relies on value-iteration (VI) algorithms. Since basic VI does not provide guarantees on the precision of the result, variants of VI have been proposed that offer such guarantees. In particular, sound value iteration (SVI) not only provides precise lower and upper bounds on the result, but also converges faster in the presence of probabilistic cycles. Unfortunately, it is neither applicable to SG, nor …

Revisiting Stochastic Collocation with Exponential Splines for an Arbitrage-Free Interpolation of Option Prices
Fabien Le Floc'h
https://arxiv.org/abs/2508.12419 https://

Revisiting Stochastic Collocation with Exponential Splines for an Arbitrage-Free Interpolation of Option Prices
We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix the abscissae and optimize the parameters of a B-spline representation.

Synchronous polarization switching at sub-coercive fields through stochastic resonance in ferroelectric thin-film capacitors
Vivek Dey, Thejas Basavarajappa, Manikantan R. S., Kevin Renji Jacob, Jonnalagadda Nikhila, Arvind Ajoy, Pavan Nukala
https://arxiv.org/abs/2508.12017

Synchronous polarization switching at sub-coercive fields through stochastic resonance in ferroelectric thin-film capacitors
Stochastic resonance (SR) is a phenomenon by which the presence of noise in a non-linear system allows for detection of a weak sub-threshold signal, or in a bi-stable system allows for sub-coercive switching between the two states. Simple theory suggests that SR occurs when the Kramers rate (rk) of the bistable system, which is a function of noise and applied voltage, is twice the drive frequency (fsignal). Here, we demonstrate the synchronous switching of polarization with a sub-coercive volta…

Network stochastic resonance under higher-order interactions
Zheng Wang, Jinjie Zhu, Xianbin Liu
https://arxiv.org/abs/2509.14796 https://arxiv.org/pdf/250…

Network stochastic resonance under higher-order interactions
Although stochastic resonance phenomena are ubiquitous across various complex systems, the influence mechanisms of higher-order interactions remain elusive. Here, we address this gap by investigating stochastic resonance in coupled phase oscillators with triadic interactions on ring networks that feature periodic modulation of the triadic coupling strength and additive noise. Our analysis reveals that higher-order interactions create fundamentally different resonance landscapes through time-var…

Once-in-a-lifetime encounter models for neutrino media II: Quasi-steady states and miscidynamic flavor evolution
Anson Kost (UNM), Lucas Johns (LANL), Huaiyu Duan (UNM)
https://arxiv.org/abs/2508.14331

Once-in-a-lifetime encounter models for neutrino media II: Quasi-steady states and miscidynamic flavor evolution
We extended the once-in-a-lifetime encounter (OILE) model to stochastic interactions among neutrinos. As in the original OILE model, the new model reproduces the mean-field behavior of a dense neutrino gas for time $t\lesssim (μγ)^{-1}$, where $μ$ measures the strength of the mean-field neutrino self-interaction potential and is proportional to the neutrino density, and the dimensionless "impact parameter" $γ$ is a measure of the change in the flavor quantum state of a neutrino during inter…

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 …

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…

Optimal Unpredictable Control for Linear Systems
Chendi Qu, Jianping He, Jialun Li, Xiaoming Duan
https://arxiv.org/abs/2508.14686 https://arxiv.org/pdf/25…

Optimal Unpredictable Control for Linear Systems
In this paper, we investigate how to achieve the unpredictability against malicious inferences for linear systems. The key idea is to add stochastic control inputs, named as unpredictable control, to make the outputs irregular. The future outputs thus become unpredictable and the performance of inferences is degraded. The major challenges lie in: i) how to formulate optimization problems to obtain an optimal distribution of stochastic input, under unknown prediction accuracy of the adversary; a…

A Universal Banach--Bregman Framework for Stochastic Iterations: Unifying Stochastic Mirror Descent, Learning and LLM Training
Johnny R. Zhang (Independent Researcher), Xiaomei Mi (University of Manchester), Gaoyuan Du (Amazon), Qianyi Sun (Microsoft), Shiqi Wang (Meta), Jiaxuan Li (Amazon), Wenhua Zhou (Independent Researcher)
https://arx…

A Universal Banach--Bregman Framework for Stochastic Iterations: Unifying Stochastic Mirror Descent, Learning and LLM Training
Stochastic optimization powers the scalability of modern artificial intelligence, spanning machine learning, deep learning, reinforcement learning, and large language model training. Yet, existing theory remains largely confined to Hilbert spaces, relying on inner-product frameworks and orthogonality. This paradigm fails to capture non-Euclidean settings, such as mirror descent on simplices, Bregman proximal methods for sparse learning, natural gradient descent in information geometry, or Kullb…

Right and Wrong Ans\"atze for Nonlinear Waves in Stochastic PDEs
C. H. S. Hamster
https://arxiv.org/abs/2508.12786 https://arxiv.org/pdf/2508.12786

Right and Wrong Ansätze for Nonlinear Waves in Stochastic PDEs
I investigate the possibility that explicit solutions of stochastic reaction-diffusion equations can be found by multiplying the deterministic travelling waves with a stochastic exponent. This approach has become widespread in the literature in recent years. I will conclude that this approach is, in general, not a valid Ansatz and only works in the case of NLS-type equations in the Stratonovich interpretation.

Stochastic Streets: A Walk Through Random LLM Address Generation in four European Cities
Tairan Fu, David Campo-Nazareno, Javier Coronado-Bl\'azquez, Javier Conde, Pedro Reviriego, Fabrizio Lombardi
https://arxiv.org/abs/2509.12914

Stochastic Streets: A Walk Through Random LLM Address Generation in four European Cities
Large Language Models (LLMs) are capable of solving complex math problems or answer difficult questions on almost any topic, but can they generate random street addresses for European cities?

Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks
Moyi Tian, P. Jeffrey Brantingham, Nancy Rodr\'iguez
https://arxiv.org/abs/2507.13310

Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks
Social media is transforming various aspects of offline life, from everyday decisions such as dining choices to the progression of conflicts. In this study, we propose a coupled modelling framework with an online social network layer to analyse how engagement on a specific topic spills over into offline protest activities. We develop a stochastic model and derive several mean-field models of varying complexity. These models allow us to estimate the reproductive number and anticipate when surges…

Stochastic Multistability of Clonallike States in the Eigen Model: a Fidelity Catastrophe
Emanuele Crosato, Richard E. Spinney, Richard G. Morris
https://arxiv.org/abs/2508.12871

Stochastic Multistability of Clonallike States in the Eigen Model: a Fidelity Catastrophe
The Eigen model is a prototypical toy model of evolution that is synonymous with the so-called error catastrophe: when mutation rates are sufficiently high, the genetic variant with the largest replication rate does not occupy the largest fraction of the total population because it acts as a source for the other variants. Here we show that, in the stochastic version of the Eigen model, there is also a fidelity catastrophe. This arises due to the state-dependence of fluctuations and occurs when …

An optimal experimental design approach to sensor placement in continuous stochastic filtering
Sahani Pathiraja, Claudia Schillings, Philipp Wacker
https://arxiv.org/abs/2508.12288

An optimal experimental design approach to sensor placement in continuous stochastic filtering
Sequential filtering and spatial inverse problems assimilate data points distributed either temporally (in the case of filtering) or spatially (in the case of spatial inverse problems). Sometimes it is possible to choose the position of these data points (which we call sensors here) in advance, with the goal of maximising the expected information gain (or a different metric of performance) from future data, and this leads to an Optimal Experimental Design (OED) problem. Here we revisit an inter…

Adversarial robustness through Lipschitz-Guided Stochastic Depth in Neural Networks
Laith Nayal, Mahmoud Mousatat, Bader Rasheed
https://arxiv.org/abs/2509.10298 https://…

Adversarial robustness through Lipschitz-Guided Stochastic Depth in Neural Networks
Deep neural networks and Vision Transformers achieve state-of-the-art performance in computer vision but are highly vulnerable to adversarial perturbations. Standard defenses often incur high computational cost or lack formal guarantees. We propose a Lipschitz-guided stochastic depth (DropPath) method, where drop probabilities increase with depth to control the effective Lipschitz constant of the network. This approach regularizes deeper layers, improving robustness while preserving clean accur…

Superparamagnetic and Stochastic-Write Magnetic Tunnel Junctions for High-Speed True Random Number Generation in Advanced Computing
Jonathan Z. Sun, Christopher Safranski, Siyuranga Koswata, Pouya Hashemi, Andrew D. Kent
https://arxiv.org/abs/2509.13469

Superparamagnetic and Stochastic-Write Magnetic Tunnel Junctions for High-Speed True Random Number Generation in Advanced Computing
We review two magnetic tunnel junction (MTJ) approaches for compact, low-power, CMOS-integrated true random number generation (TRNG). The first employs passive-read, easy-plane superparamagnetic MTJs (sMTJs) that generate thermal-fluctuation-driven bit streams at $0.5$--$1$~Gb/s per device. The second uses MTJs with magnetically stable free layers, operated with stochastic write pulses to achieve switching probabilities of about $0.5$ (\emph{i.e.}, write error rates of $\simeq 0.5$), achieving …

Muon tracking in a LiquidO opaque scintillator detector
LiquidO Collaboration, J. Apilluelo, L. Asquith, E. F. Bannister, N. P. Barradas, C. L. Baylis, J. L. Beney, M. Berberan e Santos, X. de la Bernardie, T. J. C. Bezerra, M. Bongrand, C. Bourgeois, D. Breton, J. Busto, A. Cabrera, A. Cadiou, E. Calvo, M. de Carlos Generowicz, E. Chauveau, B. J. Cattermole, M. Chen, P. Chimenti, D. F. Cowen, S. Kr. Das, S. Dusini, A. Earle, M. Felizardo, C. Frigerio Martins, J. Gal\'an, J. A. Gar…

Muon tracking in a LiquidO opaque scintillator detector
LiquidO is an innovative radiation detector concept. The core idea is to exploit stochastic light confinement in a highly scattering medium to self-segment the detector volume. In this paper, we demonstrate event-by-event muon tracking in a LiquidO opaque scintillator detector prototype. The detector consists of a 30 mm cubic scintillator volume instrumented with 64 wavelength-shifting fibres arranged in an 8$\times$8 grid with a 3.2 mm pitch and read out by silicon photomultipliers. A wax-base…

Strong overlap of deterministic and stochastic dynamics in a super-diffusive regime
Muhammad Tayyab, Jahanzeb Tariq
https://arxiv.org/abs/2508.12091 https://

Strong overlap of deterministic and stochastic dynamics in a super-diffusive regime
We consider deterministic dynamics, known as the slicer map (SM), which exhibits normal and anomalous diffusion by varying a single parameter. The statistics of the position moments and the low-order position autocorrelation function (PACF) of the SM closely overlap with those of a stochastic process called the Lévy-Lorentz gas (LLg), particularly in the normal and strongly superdiffusive anomalous regimes. However, matching low-order statistics alone cannot fully characterize the microscopic …

Differential Privacy in Kernelized Contextual Bandits via Random Projections
Nikola Pavlovic, Sudeep Salgia, Qing Zhao
https://arxiv.org/abs/2507.13639 htt…

Differential Privacy in Kernelized Contextual Bandits via Random Projections
We consider the problem of contextual kernel bandits with stochastic contexts, where the underlying reward function belongs to a known Reproducing Kernel Hilbert Space. We study this problem under an additional constraint of Differential Privacy, where the agent needs to ensure that the sequence of query points is differentially private with respect to both the sequence of contexts and rewards. We propose a novel algorithm that achieves the state-of-the-art cumulative regret of $\widetilde{\mat…

HOPSO: A Robust Classical Optimizer for VQE
Ijaz Ahamed Mohammad, Yury Chernyak, Martin Plesch
https://arxiv.org/abs/2508.13651 https://arxiv.org/pdf/2508.…

HOPSO: A Robust Classical Optimizer for VQE
Variational Quantum Eigensolver (VQE) algorithm is one of few approaches where the hope for near-term quantum advantage concentrates. However, they face challenges connected with measurement stochastic noise, barren plateaus, and optimization difficulties in periodic parameter spaces. While most of the efforts concentrates on optimizing the quantum part of the procedure, here we aim to enhance the classical optimization by utilizing a modified version of Harmonic Oscillator-based Particle Swarm…

Malliavin Calculus and Stochastic Differential Equations
Shizan Fang, Rongrong Tian
https://arxiv.org/abs/2507.13747 https://arxiv.or…

Malliavin Calculus and Stochastic Differential Equations
This paper is devoted to a study on SDEs with a bounded Borel drift b. We first remark that the original integration by parts formula due to P. Malliavin can be used to deal with derivatives with respect to space variables, then we obtain a link between the product of heat kernels and iterated divergences in Malliavin calculus. An explicit estimate for the derivative of solutions to SDE is obtained in terms of the L-infinity norm of b; as a result, we prove that the SDE defines a continuous flo…

On Tackling High-Dimensional Nonconvex Stochastic Optimization via Stochastic First-Order Methods with Non-smooth Proximal Terms and Variance Reduction
Yue Xie, Jiawen Bi, Hongcheng Liu
https://arxiv.org/abs/2509.13992

On Tackling High-Dimensional Nonconvex Stochastic Optimization via Stochastic First-Order Methods with Non-smooth Proximal Terms and Variance Reduction
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear dependence, we adopt non-Euclidean settings and propose two choices of nonsmooth proximal terms when taking the stochastic gradient steps. This approach leads to stronger convergence metric, incremental computational overhead, and potentially dimension-insensitive …

Diffuse emission from stochastic sources
Anton Stall, Philipp Mertsch
https://arxiv.org/abs/2509.14776 https://arxiv.org/pdf/2509.14776

Diffuse emission from stochastic sources
Diffuse emission in gamma-rays and neutrinos are produced by the interaction of cosmic rays with the interstellar medium. Below some hundreds of TeV, the sources of these cosmic rays are most likely Galactic. Hence, observations of high-energy gamma-rays and neutrinos can be used to probe the flux of cosmic rays in other parts of the Galaxy. Supernova remnants are usually considered as the prime candidate for the acceleration of Galactic cosmic rays. They inject cosmic rays in a point-like and …

Stochastic Modeling of Filtration with Sieving in Graded Pore Networks
Binan Gu, Pejman Sanaei, Lou Kondic, Linda J. Cummings
https://arxiv.org/abs/2508.11820 https://

Stochastic Modeling of Filtration with Sieving in Graded Pore Networks
We model filtration of a feed solution, containing both small and large foulant particles, by a membrane filter. The membrane interior is modeled as a network of pores, allowing for the simultaneous adsorption of small particles and sieving of large particles, two fouling mechanisms typically observed during the early stages of commercial filtration applications. In our model, first-principles continuum partial differential equations model transport of the small particles and adsorptive fouling…

Learning Constraints from Stochastic Partially-Observed Closed-Loop Demonstrations
Chih-Yuan Chiu, Zhouyu Zhang, Glen Chou
https://arxiv.org/abs/2509.15109 https://

Learning Constraints from Stochastic Partially-Observed Closed-Loop Demonstrations
We present an algorithm for learning unknown parametric constraints from locally-optimal input-output trajectory data. We assume that the given data is generated by demonstrators with stochastic nonlinear dynamics who execute a state or output feedback law to robustly satisfy the constraints despite worst-case dynamics and output noise. We encode the Karush-Kuhn-Tucker (KKT) conditions of this robust optimal output feedback control problem within a feasibility problem to recover constraints con…

Well posedness and propagation of chaos for multi-agent models with strategies and diffusive effects
Alessandro Baldi, Marco Morandotti
https://arxiv.org/abs/2507.14058

Well posedness and propagation of chaos for multi-agent models with strategies and diffusive effects
A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy, over a compact metric space. The evolution is governed by a non-local interaction mechanism and by stochastic effects acting on the spatial component of the state. The well-posedness of the multi-agent system and that of a certain McKean--Vlasov stochastic diffe…

Stochastic ion emission perturbation mechanisms in atom probe tomography: Linking simulations to experiment
Aslam Shaikh, Tero M\"akinen, Fran\c{c}ois Vurpillot, Mikko Alava, Ivan Lomakin
https://arxiv.org/abs/2509.13744

Stochastic ion emission perturbation mechanisms in atom probe tomography: Linking simulations to experiment
Field evaporation in atom probe tomography (APT) includes known processes related to surface migration of atoms, such as the so-called roll-up mechanism. They lead to trajectory aberrations and artefacts on the detector. These processes are usually neglected in simulations. The inclusion of such processes is crucial for providing reliable models for the development and verification of APT reconstruction algorithms, a key part of the whole methodology. Here we include stochastic lateral velocity…

Searching for continuous gravitational waves in the Parkes Pulsar Timing Array DR3
Shi-Yi Zhao, Zu-Cheng Chen, Jacob Cardinal Tremblay, Boris Goncharov, Xing-Jiang Zhu, N. D. Ramesh Bhat, Ma{\l}gorzata Cury{\l}o, Shi Dai, Valentina Di Marco, Hao Ding, George Hobbs, Agastya Kapur, Wenhua Ling, Tao Liu, Rami Mandow, Saurav Mishra, Daniel J. Reardon, Christopher J Russell, Ryan M. Shannon, Shuangqiang Wang, Lei Zhang, Andrew Zic

Searching for continuous gravitational waves in the Parkes Pulsar Timing Array DR3
We present results from an all-sky search for continuous gravitational waves from individual supermassive binary black holes using the third data release (DR3) of the Parkes Pulsar Timing Array (PPTA). Even though we recover a common-spectrum stochastic process, potentially induced by a nanohertz gravitational wave background, we find no evidence of continuous waves. Therefore, we place upper limits on the gravitational-wave strain amplitude: in the most sensitive frequency range around 10 nHz,…

A Review of Modern Stochastic Modeling: SDE/SPDE Numerics, Data-Driven Identification, and Generative Methods with Applications in Biology and Epidemiology
Yassine Sabbar
https://arxiv.org/abs/2508.11004

A Review of Modern Stochastic Modeling: SDE/SPDE Numerics, Data-Driven Identification, and Generative Methods with Applications in Biology and Epidemiology
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2) learning key parts of those models directly from data; (3) methods that can generate realistic synthetic data in continuous time; and (4) numerical techniques that keep simulations stable, accurate, and faithful over long runs. The objective is practical: help r…

Stochastic star formation activity of galaxies within the first billion years probed by JWST
C. Carvajal-Bohorquez, L. Ciesla, N. Laporte, M. Boquien, V. Buat, O. Ilbert, G. Aufort, M. Shuntov, C. Witten, P. A. Oesch, A. Covelo-Paz
https://arxiv.org/abs/2507.13160

Stochastic star formation activity of galaxies within the first billion years probed by JWST
JWST highlighted an excess of UV-bright galaxies at z>10, with a derived UVLF that exhibits a softer evolution than expected. In this work, we aim at characterizing the burstiness level of high-redshift galaxy SFHs and its evolution. We implement a stochastic SFH module in CIGALE using power spectrum densities, to estimate the burstiness level of star formation in galaxies at 66 galaxies, while smoother a…

An Adaptive Sampling Algorithm for Level-set Approximation
Matteo Croci, Abdul-Lateef Haji-Ali, Ian C. J. Powell
https://arxiv.org/abs/2509.14896 https://a…

An Adaptive Sampling Algorithm for Level-set Approximation
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which automatically refines the approximation over regions close to the level set. This strategy combines a local function approximation method with a noise reduction scheme and produces $\varepsilon$-accurate approximations with an expected cost complexity reduction of $\v…

Reactive Users vs. Recommendation Systems: An Adaptive Policy to Manage Opinion Drifts
Atefeh Mollabagher, Parinaz Naghizadeh
https://arxiv.org/abs/2508.13473 https://

Reactive Users vs. Recommendation Systems: An Adaptive Policy to Manage Opinion Drifts
Recommendation systems are used in a range of platforms to maximize user engagement through personalization and the promotion of popular content. It has been found that such recommendations may shape users' opinions over time. In this paper, we ask whether reactive users, who are cognizant of the influence of the content they consume, can prevent such changes by adaptively adjusting their content consumption choices. To this end, we study users' opinion dynamics under two types of stochastic po…

Mean Field Stochastic Partial Differential Equations with Nonlinear Kernels
Wei Hong, Shihu Li, Wei Liu
https://arxiv.org/abs/2508.12547 https://arxiv.org/…

Mean Field Stochastic Partial Differential Equations with Nonlinear Kernels
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the variational framework, then establish the convergence (in certain Wasserstein metric) of the empirical laws of interacting systems to the law of solutions of mean field equations, as the number of particles tends to infinity. The main challenge lies in address…

Learning general pair interactions between self-propelled particles
J\'er\^ome Hem, Alexis Poncet, Pierre Ronceray, Daiki Nishiguchi, Vincent D\'emery
https://arxiv.org/abs/2507.13667

Learning general pair interactions between self-propelled particles
Synthetic active matter systems, such as active colloids, often have complex interactions, which can be of hydrodynamic, chemical or electrostatic origin and cannot be computed from first principles. Here, we use Stochastic Force Inference to learn general pair interactions, including transverse forces and torques, between self-propelled Janus particles from experimental trajectories. We use data from two experiments: one where the particles flock, and one where the system remains disordered. T…

Error exponents for tripartite-to-bipartite entanglement transformations
P\'eter Vrana
https://arxiv.org/abs/2507.13778 https://a…

Error exponents for tripartite-to-bipartite entanglement transformations
We consider distillation of ebits between a specified pair of subsystems from pure tripartite states by local operations and classical communication. It is known that, allowing an asymptotically vanishing error, the maximal rate is the minimum of the von Neumann entropies of the two corresponding marginals, and under asymptotic stochastic local operations and classical communication the maximal rate is given by a minimization over a one-parameter family of entanglement measures. In this paper, …

Cooperative SGD with Dynamic Mixing Matrices
Soumya Sarkar, Shweta Jain
https://arxiv.org/abs/2508.14565 https://arxiv.org/pdf/2508.14565

Cooperative SGD with Dynamic Mixing Matrices
One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A substantial number of works in the distributed SGD setting assume a fixed topology for the edge devices. These papers also assume that the contribution of nodes to the global model is uniform. However, experiments have shown that such assumptions are suboptimal …

Impact of homophily in adherence to anti-epidemic measures on the spread of infectious diseases in social networks
Piotr Bentkowski, Tomasz Gubiec
https://arxiv.org/abs/2507.13848

Impact of homophily in adherence to anti-epidemic measures on the spread of infectious diseases in social networks
We investigate how homophily in adherence to anti-epidemic measures affects the final size of epidemics in social networks. Using a modified SIR model, we divide agents into two behavioral groups-compliant and non-compliant-and introduce transmission probabilities that depend asymmetrically on the behavior of both the infected and susceptible individuals. We simulate epidemic dynamics on two types of synthetic networks with tunable inter-group connection probability: stochastic block models (SB…

A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon
Qingmeng Wei, Jiongmin Yong
https://arxiv.org/abs/2509.14495 https://arx…

A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon
This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time. Under such a condition, the problem in an infinite time horizon can be decomposed into two parts: a non-autonomous time-consistent problem in an infinite time horizon and a time-inconsistent problem in a finite time horizon. Then an equilibrium strategy will be …

Pairwise correlations of global times in one-dimensional Brownian motion under stochastic resetting
Yihao Wang, Hanshuang Chen
https://arxiv.org/abs/2508.11387 https://

Pairwise correlations of global times in one-dimensional Brownian motion under stochastic resetting
Brownian motion with stochastic resetting-a process combining standard diffusion with random returns to a fixed position-has emerged as a powerful framework with applications spanning statistical physics, chemical kinetics, biology, and finance. In this study, we investigate the mutual correlations among three global characteristic times for one-dimensional resetting Brownian motion $x(τ)$ over the interval $τ\in \left[ 0, t\right] $: the occupation time $t_o$ spent on the positive semi-axis,…

Physics constrained learning of stochastic characteristics
Pardha Sai Krishna Ala, Ameya Salvi, Venkat Krovi, Matthias Schmid
https://arxiv.org/abs/2507.12661

Physics constrained learning of stochastic characteristics
Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An error in the selection of covariance matrices could impact the accuracy of the estimation algorithm and may sometimes cause the filter to diverge. Identifying noise characteristics has long been a challenging problem due to uncertainty surrounding noise sourc…

Categorical Policies: Multimodal Policy Learning and Exploration in Continuous Control
SM Mazharul Islam, Manfred Huber
https://arxiv.org/abs/2508.13922 https://

Categorical Policies: Multimodal Policy Learning and Exploration in Continuous Control
A policy in deep reinforcement learning (RL), either deterministic or stochastic, is commonly parameterized as a Gaussian distribution alone, limiting the learned behavior to be unimodal. However, the nature of many practical decision-making problems favors a multimodal policy that facilitates robust exploration of the environment and thus to address learning challenges arising from sparse rewards, complex dynamics, or the need for strategic adaptation to varying contexts. This issue is exacerb…

Crosslisted article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
- Stochastic Modeling of Filtration with Sieving in Graded Pore Networks
Binan Gu, Pejman Sanaei, Lou Kondic, Linda J. Cummings

Sequential test sampling for stochastic derivative-free optimization
Anjie Ding, Francesco Rinaldi, Luis Nunes Vicente
https://arxiv.org/abs/2509.14505 https://

Sequential test sampling for stochastic derivative-free optimization
In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial step, i.e., the true reduction in the objective function value that would be achieved by moving from the current point to the trial point, be larger than a multiple of the squared stepsize. When the objective function is stochastic, evaluating such a condition…

Targeted search for an individual SMBHB in NANOGrav 15-year and EPTA DR2 data sets
Li-Wen Tian, Yan-Chen Bi, Yu-Mei Wu, Qing-Guo Huang
https://arxiv.org/abs/2508.14742 https://

Targeted search for an individual SMBHB in NANOGrav 15-year and EPTA DR2 data sets
While pulsar timing array (PTA) collaborations have reported evidence for a stochastic gravitational wave background (GWB), the detection of continuous gravitational waves (GWs) from a confirmed supermassive black hole binary (SMBHB) would provide strong support for the SMBHB origin of GWB. In this study, we analyze continuous GWs from the SMBHB candidate 3C 66B, modeling the GWB as a common uncorrelated red noise. Using Bayesian methods, we perform targeted searches across two PTA data sets: N…

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…

Stochastic Hamiltonian Type Jump Diffusion Systems with Countable Regimes: Strong Feller Property and Exponential Ergodicity
Fubao Xi, Yafei Zhai, Zuozheng Zhang
https://arxiv.org/abs/2509.14951

Stochastic Hamiltonian Type Jump Diffusion Systems with Countable Regimes: Strong Feller Property and Exponential Ergodicity
This work focuses on a class of stochastic Hamiltonian type jump diffusion systems with state-dependent switching, in which the switching component has countably infinite many states.First, the existence and uniqueness of the underlying processes are obtained with the aid of successive construction methods. Then, the Feller property is established by coupling methods. Furthermore, the strong Feller property is proved by introducing some auxiliary processes and making use of appropriate Radon-Ni…

A Neural Column-and-Constraint Generation Method for Solving Two-Stage Stochastic Unit Commitment
Zhentong Shao, Jingtao Qin, Nanpeng Yu
https://arxiv.org/abs/2508.11071 https:/…

A Neural Column-and-Constraint Generation Method for Solving Two-Stage Stochastic Unit Commitment
Two-stage stochastic unit commitment (2S-SUC) problems have been widely adopted to manage the uncertainties introduced by high penetrations of intermittent renewable energy resources. While decomposition-based algorithms such as column-and-constraint generation has been proposed to solve these problems, they remain computationally prohibitive for large-scale, real-time applications. In this paper, we introduce a Neural Column-and-Constraint Generation (Neural CCG) method to significantly accele…

Order Optimal Regret Bounds for Sharpe Ratio Optimization in the Bandit Setting
Mohammad Taha Shah, Sabrina Khurshid, Gourab Ghatak
https://arxiv.org/abs/2508.13749 https://

Order Optimal Regret Bounds for Sharpe Ratio Optimization in the Bandit Setting
In this paper, we investigate the problem of sequential decision-making for Sharpe ratio (SR) maximization in a stochastic bandit setting. We focus on the Thompson Sampling (TS) algorithm, a Bayesian approach celebrated for its empirical performance and exploration efficiency, under the assumption of Gaussian rewards with unknown parameters. Unlike conventional bandit objectives focusing on maximizing cumulative reward, Sharpe ratio optimization instead introduces an inherent tradeoff between a…

A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production
Alexander M. Maier, Jonas H. Fritz, Udo Seifert
https://arxiv.org/abs/2509.15077

A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production
Semi-Markov processes play an important role in the effective description of partially accessible systems in stochastic thermodynamics. They occur, for instance, in coarse-graining procedures such as state lumping and when analyzing waiting times between few visible Markovian events. The finite-time measurement of any coarse-grained observable in a stochastic system depends on the specific realization of the underlying trajectory. Moreover, the fluctuations of such observables are encoded in th…

BSDE Approach for $\alpha$-Potential Stochastic Differential Games
Xin Guo, Xun Li, Liangquan Zhang
https://arxiv.org/abs/2507.13256 https://

BSDE Approach for $α$-Potential Stochastic Differential Games
In this paper, we examine a class of $α$-potential stochastic differential games with random coefficients via the backward stochastic differential equations (BSDEs) approach. Specifically, we show that the first and second order linear derivatives of the objective function for each player can be expressed through the corresponding first and second-order adjoint equations, which leads to rigorous estimates for $α$. We illustrate the dependence of $α$ on game characteristics through detailed a…

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…

Reinforcement Learning-based Adaptive Path Selection for Programmable Networks
Jos\'e Eduardo Zerna Torres, Marios Avgeris, Chrysa Papagianni, Gergely Pongr\'acz, Istv\'an G\'odor, Paola Grosso
https://arxiv.org/abs/2508.13806

Reinforcement Learning-based Adaptive Path Selection for Programmable Networks
This work presents a proof-of-concept implementation of a distributed, in-network reinforcement learning (IN-RL) framework for adaptive path selection in programmable networks. By combining Stochastic Learning Automata (SLA) with real-time telemetry data collected via In-Band Network Telemetry (INT), the proposed system enables local, data-driven forwarding decisions that adapt dynamically to congestion conditions. The system is evaluated on a Mininet-based testbed using P4-programmable BMv2 sw…

Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line
Robert C. Dalang, David Nualart, Fei Pu
https://arxiv.org/abs/2508.11859

Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line
For Gaussian random fields with values in $\mathbb{R}^d$, sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in particular to the solutions of systems of linear SPDEs. For non-Gaussian random fields, the available bounds are less sharp. For nonlinear systems of stochastic heat equations, a sharp lower bound was obtained in a previous paper by two of the authors. Here, we obtain the corresponding sharp upper bound. The proof req…

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…

A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization
Olga Turanova, Yuming Paul Zhang
https://arxiv.org/abs/2508.13441 https://

A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization
We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set. Our contributions are twofold. First, we establish well-posedness and a comparison principle for the problem by introducing a novel notion of viscosity flows. Second, under the assumption that the coefficients are stationary ergodic, we prove a stochastic homogenization result. Our results are new even in the period…

Metastability in the parallel Ising model
Franco Bagnoli, Tommaso Matteuzzi
https://arxiv.org/abs/2508.13168 https://arxiv.org/pdf/2508.13168

Metastability in the parallel Ising model
In this short paper we present some considerations about some parallel implementations of the dynamic (Monte Carlo) version of the Ising model. In some cases the equilibrium distribution of the parallel version does not present the symmetry breaking phenomenon in the low-temperature phase, i.e., the stochastic trajectory originated by the Monte Carlo simulation can jump between the distributions corresponding to both kinds of magnetization, or the lattice can break into two disjoint sublattices…

Heavy-tailed Linear Bandits: Adversarial Robustness, Best-of-both-worlds, and Beyond
Canzhe Zhao, Shinji Ito, Shuai Li
https://arxiv.org/abs/2508.13679 https://

Heavy-tailed Linear Bandits: Adversarial Robustness, Best-of-both-worlds, and Beyond
Heavy-tailed bandits have been extensively studied since the seminal work of \citet{Bubeck2012BanditsWH}. In particular, heavy-tailed linear bandits, enabling efficient learning with both a large number of arms and heavy-tailed noises, have recently attracted significant attention \citep{ShaoYKL18,XueWWZ20,ZhongHYW21,Wang2025heavy,tajdini2025improved}. However, prior studies focus almost exclusively on stochastic regimes, with few exceptions limited to the special case of heavy-tailed multi-arm…

Stochastic Entanglement Configuration for Constructive Entanglement Topologies in Quantum Machine Learning with Application to Cardiac MRI
Mehri Mehrnia, Mohammed S. M. Elbaz
https://arxiv.org/abs/2507.11401

Stochastic Entanglement Configuration for Constructive Entanglement Topologies in Quantum Machine Learning with Application to Cardiac MRI
Efficient entanglement strategies are essential for advancing variational quantum circuits (VQCs) for quantum machine learning (QML). However, most current approaches use fixed entanglement topologies that are not adaptive to task requirements, limiting potential gains over classical models. We introduce a novel stochastic entanglement configuration method that systematically generates diverse entanglement topologies to identify a subspace of constructive entanglement configurations, defined as…

On the Gaussian Limit of the Output of IIR Filters
Yashaswini Murthy, Bassam Bamieh, R. Srikant
https://arxiv.org/abs/2508.12705 https://arxiv.org/pdf/2508…

On the Gaussian Limit of the Output of IIR Filters
We study the asymptotic distribution of the output of a stable Linear Time-Invariant (LTI) system driven by a non-Gaussian stochastic input. Motivated by longstanding heuristics in the stochastic describing function method, we rigorously characterize when the output process becomes approximately Gaussian, even when the input is not. Using the Wasserstein-1 distance as a quantitative measure of non-Gaussianity, we derive upper bounds on the distance between the appropriately scaled output and a …

Stochastic Weakly Convex Optimization Under Heavy-Tailed Noises
Tianxi Zhu, Yi Xu, Xiangyang Ji
https://arxiv.org/abs/2507.13283 https://

Stochastic Weakly Convex Optimization Under Heavy-Tailed Noises
An increasing number of studies have focused on stochastic first-order methods (SFOMs) under heavy-tailed gradient noises, which have been observed in the training of practical deep learning models. In this paper, we focus on two types of gradient noises: one is sub-Weibull noise, and the other is noise under the assumption that it has a bounded $p$-th central moment ($p$-BCM) with $p\in (1, 2]$. The latter is more challenging due to the occurrence of infinite variance when $p\in (1, 2)$. Under…

Quantum algorithm for solving McKean-Vlasov stochastic differential equations
Koichi Miyamoto
https://arxiv.org/abs/2507.10926 https://

Quantum algorithm for solving McKean-Vlasov stochastic differential equations
Quantum Monte Carlo integration, a quantum algorithm for calculating expectations that provides a quadratic speed-up compared to its classical counterpart, is now attracting increasing interest in the context of its industrial and scientific applications. In this paper, we propose the first application of QMCI to solving McKean-Vlasov stochastic differential equations (MVSDEs), a nonlinear class of SDEs whose drift and diffusion coefficients depend on the law $μ_t$ of the solution $X_t$ -- app…

Distributed Multiple Fault Detection and Estimation in DC Microgrids with Unknown Power Loads
Jingwei Dong, Mahdieh S. Sadabadi, Per Mattsson, Andr\'e Teixeira
https://arxiv.org/abs/2508.14675

Distributed Multiple Fault Detection and Estimation in DC Microgrids with Unknown Power Loads
This paper proposes a distributed diagnosis scheme to detect and estimate actuator and power line faults in DC microgrids subject to unknown power loads and stochastic noise. To address actuator faults, we design a fault estimation filter whose parameters are determined through a tractable optimization problem to achieve fault estimation, decoupling from power line faults, and robustness against noise. In contrast, the estimation of power line faults poses greater challenges due to the inherent…

Faster stochastic cubic regularized Newton methods with momentum
Yiming Yang, Chuan He, Xiao Wang, Zheng Peng
https://arxiv.org/abs/2507.13003 https://

Faster stochastic cubic regularized Newton methods with momentum
Cubic regularized Newton (CRN) methods have attracted signiffcant research interest because they offer stronger solution guarantees and lower iteration complexity. With the rise of the big-data era, there is growing interest in developing stochastic cubic regularized Newton (SCRN) methods that do not require exact gradient and Hessian evaluations. In this paper, we propose faster SCRN methods that incorporate gradient estimation with small, controlled errors and Hessian estimation with momentum…

Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching
Fubao Xi, Mingkun Ye, Zuozheng Zhang
https://arxiv.org/abs/2509.13665

Well-Posedness and Ergodicity of Functional Stochastic Partial Differential Equations with Markovian Switching
This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying process is obtained by Skorokhod's representation of the switching component. Then, the exponential mixing of such processes in a finite state space is derived by using the so-called remote start method proposed firstly by Prato and Zabczyk in [10]. Finally, t…

Trust Region Algorithm for Stochastic Minimax Problems with Decision-Dependent Distributions
Yan Gao, Yongchao Liu, Zili Luo
https://arxiv.org/abs/2509.12868 https://

Trust Region Algorithm for Stochastic Minimax Problems with Decision-Dependent Distributions
Stochastic minimax optimization has drawn much attention over the past decade due to its broad applications in machine learning, signal processing and game theory. In some applications, the probability distribution of uncertainty depends on decision variables, as the environment may respond to decisions. In this paper, we propose a trust region algorithm for finding the stationary points of stochastic minimax problems with decision-dependent distributions. At each iteration, the algorithm local…

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…

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…

Graph-Aware Learning Rates for Decentralized Optimization
Aaron Fainman, Stefan Vlaski
https://arxiv.org/abs/2509.14854 https://arxiv.org/pdf/2509.14854

Graph-Aware Learning Rates for Decentralized Optimization
We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly stochastic) gradients and global information (like smoothness) is unavailable. We derive a step-size rule from first principles. The resulting formulation reduces to the well-known Polyak's rule in the single-agent setting, and is suitable for use with stochastic gr…

Finite-Time Convergence Analysis of ODE-based Generative Models for Stochastic Interpolants
Yuhao Liu, Rui Hu, Yu Chen, Longbo Huang
https://arxiv.org/abs/2508.07333 https://

Finite-Time Convergence Analysis of ODE-based Generative Models for Stochastic Interpolants
Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence guarantees for practical numerical schemes remain largely unexplored. In this work, we address the finite-time convergence analysis of numerical implementations for ordinary differential equations (ODEs) derived from stochastic interpolants. Specifically, we esta…

Parameterized Controls and Isomorphic Representations of G-Expectations
Guangqian Zhao
https://arxiv.org/abs/2509.13675 https://arxiv.org/pdf/2509.13675

Parameterized Controls and Isomorphic Representations of G-Expectations
This paper establishes a fundamental isomorphism between the abstract framework of $G$-expectation and a concrete parameterized family of classical stochastic processes, providing a unified framework for nonlinear stochastic calculus under model uncertainty. We demonstrate that $G$-Brownian motion and related stochastic differential equations (SDEs) can be intrinsically represented as controlled processes $\{B_t^θ\}_{θ\in \mathcal{A}^Θ}$, where $θ$ denotes an admissible control process taki…

Accelerating Stochastic Energy System Optimization Models: Temporally Split Benders Decomposition
Shima Sasanpour, Manuel Wetzel, Karl-Ki\^en Cao, Hans Christian Gils, Andr\'es Ramos
https://arxiv.org/abs/2508.10789

Accelerating Stochastic Energy System Optimization Models: Temporally Split Benders Decomposition
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering uncertainties. For two-stage stochastic capacity expansion planning problems, Benders decomposition is often applied to ensure that the problem remains solvable. Since stochastic scenarios can be optimized independently within subproblems, their optimization can …

Crosslisted article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- Strong solutions for a class of stochastic thermo-magneto-hydrodynamic-type systems with multipli...
Agus L. Soenjaya, Thanh Tran

Crosslisted article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- Stochastic Modeling of Filtration with Sieving in Graded Pore Networks
Binan Gu, Pejman Sanaei, Lou Kondic, Linda J. Cummings

Randomized Feasibility-Update Algorithms for Stochastic Variational Inequality Problems
Abhishek Chakraborty, Angelia Nedi\'c
https://arxiv.org/abs/2509.12613 https://

Randomized Feasibility-Update Algorithms for Stochastic Variational Inequality Problems
This paper considers stochastic monotone variational inequalities whose feasible region is the intersection of a (possibly infinite) number of convex functional level sets. A projection-based approach or direct Lagrangian-based techniques for such problems can be computationally expensive if not impossible to implement. To deal with the problem, we consider randomized methods that avoid the projection step on the whole constraint set by employing random feasibility updates. In particular, we pr…

Replaced article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- Global well-posedness and small time asymptotics of stochastic Ladyzhenskaya-Smagorinsky equation...
Ankit Kumar, Manil T. Mohan

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…

A risk-sensitive ergodic singular stochastic control problem
Justin Gwee, Mihail Zervos
https://arxiv.org/abs/2509.09835 https://arxiv.org/pdf/2509.09835…

A risk-sensitive ergodic singular stochastic control problem
We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modelled by a linear diffusion. The control that can be applied to the system is modelled by an additive finite variation process. The objective of the control problem is to minimise a risk-sensitive long-term average criterion that penalises deviations of the controlled process from a given interval, as well as the e…