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We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…

Optimization and Control · Mathematics 2025-05-27 Ashley Davey , Harry Zheng

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…

Machine Learning · Computer Science 2023-07-19 Kun Yuan , Sulaiman A. Alghunaim , Bicheng Ying , Ali H. Sayed

Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…

Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…

Numerical Analysis · Mathematics 2026-01-27 Emanuel Pfarr , Radu Timofte , Frank Werner

The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost…

Methodology · Statistics 2024-02-22 L. Jeff Hong , Yingda Song , Tan Wang

In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method…

Numerical Analysis · Mathematics 2022-05-25 Liu Liu , Lorenzo Pareschi , Xueyu Zhu

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Statistics Theory · Mathematics 2007-06-13 Yacine Ait-Sahalia , Per A. Mykland

We study the Euler scheme for a stochastic differential equation driven by a Levy process Y. More precisely, we look at the asymptotic behavior of the normalized error process u_n(X^n-X), where X is the true solution and X^n is its Euler…

Probability · Mathematics 2007-05-23 Jean Jacod

This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly…

Probability · Mathematics 2017-09-26 Felix Lindner , Holger Stroot

Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a…

Numerical Analysis · Mathematics 2020-08-21 Jian Ren , Jinqiao Duan

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

Optimization and Control · Mathematics 2015-02-18 Shu-Jun Liu , Miroslav Krstic

We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and second order schemes. In order to implement the general case…

Classical Analysis and ODEs · Mathematics 2007-05-23 Peter Friz , Nicolas Victoir

We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…

Optimization and Control · Mathematics 2024-05-15 Joshua Cutler , Mateo Díaz , Dmitriy Drusvyatskiy

We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive…

Statistical Mechanics · Physics 2025-08-04 Kotaro Ikeda , Tomoya Uda , Daisuke Okanohara , Sosuke Ito

We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known…

Statistics Theory · Mathematics 2014-06-24 Valentine Genon-Catalot , Catherine Larédo

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

Optimization and Control · Mathematics 2015-03-10 Gabriel Peyré

In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…

Probability · Mathematics 2016-09-08 Young Myoung Ko , Natarajan Gautam

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

Numerical Analysis · Mathematics 2015-04-08 Bangti Jin , Raytcho Lazarov , Dongwoo Sheen , Zhi Zhou

In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…

Numerical Analysis · Mathematics 2025-11-20 Paweł Przybyłowicz , Michał Sobieraj

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…

Analysis of PDEs · Mathematics 2017-01-10 Guillaume Carlier , Vincent Duval , Gabriel Peyré , Bernhard Schmitzer