Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise

Abstract

In this article, we investigate the Wong-Zakai approximations of a class of second order non-autonomous stochastic lattice systems with additive white noise. We first prove the existence and uniqueness of tempered pullback random attractors for the original stochastic system and its Wong-Zakai approximation. Then, we establish the upper semicontinuity of these attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.

Keywords

• wong-zakai approximation
• lattice systems
• random attractor
• white noise
• upper semicontinuity