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

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.