The convergence rate of approximate center manifolds for stochastic evolution equations via a Wong-Zakai type approximation.

In this paper, we study the Wong-Zakai approximations of stochastic evolution equations driven by a multiplicative white noise and their related dynamical behavior, where the Wong-Zakai approximations are given by a stationary process via the Wiener shift. Firstly, we show that the solutions of these stochastic evolution equations can be approximated almost surely with a polynomial rate. Next, we explore the Wong-Zakai approximations on the center manifolds of these stochastic evolution equations under an exponential trichotomy condition. Finally, we prove that these approximate center manifolds converge almost surely, with a polynomial rate. [ABSTRACT FROM AUTHOR]