English
Related papers

Related papers: Averaging principle for one dimensional stochastic…

200 papers

In this paper, the averaging principle is studied for a class of multiscale stochastic partial differential equations driven by $\alpha$-stable process, where $\alpha\in(1,2)$. Using the technique of Poisson equation, the orders of strong…

Probability · Mathematics 2021-06-08 Xiaobin Sun , Yingchao Xie

In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path,…

Probability · Mathematics 2025-04-28 Yuzuru Inahama

This paper establishes the averaging method to a coupled system consisting of two stochastic differential equations which has a slow component driven by fractional Brownian motion (FBM) with less regularity $1/3< H \leq 1/2$ and a fast…

Probability · Mathematics 2023-07-26 Bin Pei , Robert Hesse , Bjoern Schmalfuss , Yong Xu

We present the validity of stochastic averaging principle for non-autonomous slow-fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from…

Probability · Mathematics 2018-12-11 Kenneth Uda

In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone…

Probability · Mathematics 2024-12-20 Sara Mazzonetto , Diyora Salimova

This paper investigates a non-autonomous slow-fast system, which is generalized by stochastic differential equations (SDEs) with locally Lipschitz coefficients, subjected to standard Brownian motion (Bm) and fractional Brownian motion (fBm)…

Probability · Mathematics 2020-12-21 Ruifang Wang , Yong Xu , Hongge Yue

In this paper, we study the averaging principle for a class of stochastic differential equations driven by $\alpha$-stable processes with slow and fast time-scales, where $\alpha\in(1,2)$. We prove that the strong and weak convergence order…

Probability · Mathematics 2021-05-11 Xiaobin Sun , Longjie Xie , Yingchao Xie

In this article we establish strong convergence rates on the whole probability space for explicit full-discrete approximations of stochastic Burgers equations with multiplicative trace-class noise. The key step in our proof is to establish…

Probability · Mathematics 2022-11-01 Martin Hutzenthaler , Robert Link

We study the one-dimensional stochastic heat equation in the mild form driven by a general stochastic measure $\mu$, for $\mu$ we assume only $\sigma$-additivity in probability. The time averaging of the equation is considered, uniform a.…

Probability · Mathematics 2018-12-14 Vadym Radchenko

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their…

Dynamical Systems · Mathematics 2013-01-22 Yong Xu , Rong Guo , Di Liu , Huiqing Zhang , Jinqiao Duan

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

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

In this project we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman-Kac…

Probability · Mathematics 2017-09-21 Peter Lewis , David Nualart

This paper investigates a class of slow--fast systems of rough partial differential equations defined over a monotone family of interpolation Hilbert spaces. By employing the controlled rough path framework tailored to a monotone family of…

Probability · Mathematics 2025-10-28 Miaomiao Li , Bin Pei , Yong Xu , Xiaole Yue

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

This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…

Probability · Mathematics 2017-09-18 Bob Pepin

Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. In this paper, we will establish an averaging principle for multiscale stochastic linearly…

Dynamical Systems · Mathematics 2017-03-14 Peng Gao , Yong Li

In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed…

Probability · Mathematics 2021-11-02 Arnulf Jentzen , Felix Lindner , Primož Pušnik

This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in…

Probability · Mathematics 2013-09-20 Martin Hairer , Jochen Voss

By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H\"{o}lder…

Probability · Mathematics 2020-03-10 Xiaobin Sun , Longjie Xie , Yingchao Xie