The Wong-Zakai approximations of invariant manifolds and foliations for stochastic evolution equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Shen, Jun¹  Zhao, Junyilang²  Lu, Kening²  Wang, Bixiang³ 

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

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

[3] New Mexico Inst Min & Technol, Dept Math, Socorro, NM 87801 USA

关键词: Wong-Zakai approximation;    Stochastic evolution equation;    Multiplicative noise;    Invariant manifolds;    Invariant foliations;   

DOI  :  10.1016/j.jde.2018.10.008

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 a class of stochastic evolution equations with a multiplicative white noise. We prove that the solutions of Wong-Zakai approximations almost surely converge to the solutions of the Stratonovich stochastic evolution equation. We also show that the invariant manifolds and stable foliations of the Wong-Zakai approximations converge to the invariant manifolds and stable foliations of the Stratonovich stochastic evolution equation, respectively. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free