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The present article deals with the averaging principle for a two-time-scale system of jump-diffusion stochastic differential equation. Under suitable conditions, the weak error is expanded in powers of timescale parameter. It is proved that…

Probability · Mathematics 2018-06-01 Bengong Zhang , Hongbo Fu , Li Wan , Jicheng Liu

Using Zvonkin's transform and the Poisson equation in $R^d$ with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent H\"older continuous coefficients. Sharp convergence rates with order…

Probability · Mathematics 2019-07-23 Michael Röckner , Xiaobin Sun , Longjie Xie

This work is concerned with fractional stochastic differential equations with different scales. We establish the existence and uniqueness of solutions for Caputo fractional stochastic differential systems under the non-Lipschitz condition.…

Numerical Analysis · Mathematics 2024-09-24 Zhaoyang Wang , Ping Lin

We show a decomposition into the sum of a martingale and a deterministic quantity for time averages of the solutions to non-autonomous SDEs and for discrete-time Markov processes. In the SDE case the martingale has an explicit…

Probability · Mathematics 2018-02-08 Bob Pepin

This paper considers a class of nonautonomous slow-fast stochastic partial differential equations driven by $\alpha$-stable processes for $\alpha\in (1,2)$. By introducing the evolution system of measures, we establish an averaging…

Probability · Mathematics 2025-07-11 Yueling Li , Xiaobin Sun , Zijuan Wang , Yingchao Xie

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $\sigma$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for…

Probability · Mathematics 2024-07-23 Vadym Radchenko

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we…

Probability · Mathematics 2022-01-21 Wei Hong , Shihu Li , Wei Liu

In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…

Dynamical Systems · Mathematics 2024-09-20 Mengyu Cheng , Zimo Hao , Xicheng Zhang

We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…

Strongly Correlated Electrons · Physics 2023-01-11 Hui Shao , Anders W. Sandvik

We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…

Probability · Mathematics 2020-11-12 Michael Röckner , Longjie Xie , Li Yang

This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$. In…

Statistics Theory · Mathematics 2016-09-30 Jianhai Bao , George Yin , Chenggui Yuan

This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…

Computational Physics · Physics 2007-05-23 Sergey Plyasunov

In this article, we investigate averaging principle for stochastic hyperbolic-parabolic equations with two time-scales, in which both the slow and fast components are perturbed by multiplicative noises. Particularly, we prove that the rate…

Probability · Mathematics 2017-12-22 Hongbo Fu , Li Wan , Jicheng Liu , Xianming Liu

In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…

Probability · Mathematics 2023-12-19 Xiaobin Sun , Yingchao Xie

In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…

Probability · Mathematics 2025-09-03 Mengyu Cheng , Xiaobin Sun , Yingchao Xie

We present, in the simplest possible form, the so called martingale problem strategy to establish limit theorems. The presentation is specially adapted to problems arising in partially hyperbolic dynamical systems. We will discuss a simple…

Dynamical Systems · Mathematics 2014-09-15 Jacopo De Simoi , Carlangelo Liverani

Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…

Probability · Mathematics 2007-05-23 Giovanni Peccati , Murad S. Taqqu

In this paper, we consider the stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps. First, under certain averaging conditions, we are able to show that the solutions of…

Probability · Mathematics 2023-08-07 Guangjun Shen , Jie Xiang , Jiang-Lun Wu

In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of…

Dynamical Systems · Mathematics 2020-07-16 Yong Xu , Ruifang Wang

We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…

Probability · Mathematics 2021-08-27 David Criens , Peter Pfaffelhuber , Thorsten Schmidt