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I played Sudokuish today after a long absence. I solved all 3 difficulties for today without too much trouble. Maybe today's puzzle set is easier than typical, or maybe I'm just smarter today.
Sudokuish #233/25
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A Hyperlogic for Strategies in Stochastic Games (Extended Version)
Lina Gerlach (RWTH Aachen University), Christof L\"oding (RWTH Aachen University), Erika \'Abrah\'am (RWTH Aachen University)
https://arxiv.org/abs/2506.16775

A Hyperlogic for Strategies in Stochastic Games (Extended Version)
We propose a probabilistic hyperlogic called HyperSt$^2$ that can express hyperproperties of strategies in turn-based stochastic games. To the best of our knowledge, HyperSt$^2$ is the first hyperlogic for stochastic games. HyperSt$^2$ can relate probabilities of several independent executions of strategies in a stochastic game. For example, in HyperSt$^2$ it is natural to formalize optimality, i.e., to express that some strategy is better than all other strategies, or to express the existence …

Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network
Chen Chen, Lijin Wang, Yanzhao Cao, Xupeng Cheng
https://arxiv.org/abs/2507.14467

Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network
In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the underlying stochastic Hamiltonian system and produces symplectic predictions. Our model utilizes the autoencoder framework to identify the randomness of the latent system by the encoder network, and detects the stochastic generating function of the system thr…

Discrete-Time LQ Stochastic Two Person Nonzero Sum Difference Games With Random Coefficients:~Closed-Loop Nash Equilibrium
Qingxin Meng, Yiwei Wu
https://arxiv.org/abs/2507.16412 …

Discrete-Time LQ Stochastic Two Person Nonzero Sum Difference Games With Random Coefficients:~Closed-Loop Nash Equilibrium
This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost functionals, leading to a complex structure of fully coupled cross-coupled stochastic Riccati equations (CCREs). The key contributions lie in characterizing the equilibrium via state-feedback strategies derived by decoupling stochastic Hamiltonian systems governe…

Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains
Minglei Yang, Yanfang Liu, Diego del-Castillo-Negrete, Yanzhao Cao, Guannan Zhang
https://arxiv.org/abs/2507.15990

Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approa…

On tail probability of the covariance matrix in Eldan's stochastic localization
Qingyang Guan
https://arxiv.org/abs/2508.14943 https://arxiv.org/pdf/25…

On tail probability of the covariance matrix in Eldan's stochastic localization
The Eldan's stochastic localization is a new kind of stochastic evolution in the space of probability measures which provides a novel way to study high dimensional convex body. A central object in the study of the stochastic localization is the stochastic process of its covariance matrix. The main result of this paper is some exponential-type tail probability estimate of the covariance process for the general time. This estimate implies a weaker version of a $p$-moment conjecture by Klartag and…

A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations
Darryl D. Holm, Maneesh Kumar Singh, Oliver D. Street
https://arxiv.org/abs/2507.14264

A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations
We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a complementary approach which preserves Casimirs of the Poisson bracket. Through an energy preserving numerical implementation of the model, we study the influence of noise on the well-known 'peakon' formation behaviour of the solution. The energy conserving stochastic approach generates an ensemble of solutions which are sp…

Time integration of dissipative stochastic PDEs
Helena Bi\v{s}\v{c}evi\'c, Raffaele D'Ambrosio
https://arxiv.org/abs/2507.16658 https://arxiv.org/p…

Time integration of dissipative stochastic PDEs
The paper is focused on the numerical solution of stochastic reaction-diffusion problems. A special attention is addressed to the conservation of mean-square dissipativity in the time integration of the spatially discretized problem, obtained by means of finite differences. The analysis highlights the conservative ability of stochastic $θ$-methods and stochastic $θ$-IMEX methods, emphasizing the roles of spatial and temporal stepsizes. A selection of numerical experiments is provided, confirm…

Differential Stochastic Variational Inequalities with Parametric Optimization
Xiaojun Chen, Jian Guo, Guan Wang
https://arxiv.org/abs/2508.15241 https://ar…

Differential Stochastic Variational Inequalities with Parametric Optimization
The differential stochastic variational inequality with parametric convex optimization (DSVI-O) is an ordinary differential equation whose right-hand side involves a stochastic variational inequality and solutions of several dynamic and random parametric convex optimization problems. We consider that the distribution of the random variable is time-dependent and assume that the involved functions are continuous and the expectation is well-defined. We show that the DSVI-O has a weak solution with…

Stabilization of jump-diffusion stochastic differential equations by hysteresis switching
Weichao Liang, Gaoyue Guo
https://arxiv.org/abs/2507.15191 https:…

Stabilization of jump-diffusion stochastic differential equations by hysteresis switching
We address the stabilization of both classical and quantum systems modeled by jump-diffusion stochastic differential equations using a novel hysteresis switching strategy. Unlike traditional methods that depend on global Lyapunov functions or require each subsystem to stabilize the target state individually, our approach employs local Lyapunov-like conditions and state-dependent switching to achieve global asymptotic or exponential stability with finitely many switches almost surely. We rigorou…