Wong-Zakai approximations of stochastic lattice systems driven by long-range interactions and multiplicative white noises

Abstract

<p style='text-indent:20px;'>In this paper, we study the Wong-Zakai approximations of a stochastic lattice differential equation with long-range interactions and multiplicative white noise at each node. We first prove the existence and uniqueness of pullback random attractors for lattice system driven by multiplicative white noises as well as the corresponding Wong-Zakai approximate system. Then, we prove the convergence of solutions and the upper semicontinuity of random attractors for the Wong-Zakai approximate system as the size of approximation approaches zero.</p>