Wong-Zakai approximations and center manifolds of stochastic differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Shen, Jun¹  Lu, Kening^1,2 

[1] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China

[2] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

关键词: Brownian motion;    Wong-Zalmi approximations;    Multiplicative noise;    Random dynamical systems;    Center manifolds;   

DOI  :  10.1016/j.jde.2017.06.005

来源: Elsevier

【 摘 要 】

In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated dynamics of the stochastic differential equation driven by a l-dimensional Brownian motion. We prove that the solutions of Wong-Zakai approximations converge in the mean square to the solutions of the Stratonovich stochastic differential equation. We also show that for a simple multiplicative noise, the center-manifold of the Wong-Zakai approximations converges to the center-manifold of the Stratonovich stochastic differential equation. (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free