Exponential Stability of Non-Autonomous Stochastic Delay Lattice Systems with Multiplicative Noise

Abstract

We study asymptotic stability of a class of non-autonomous stochastic delay lattice systems driven by a multiplicative white noise. Under certain conditions, we prove such systems have a unique tempered complete quasi-solution which exponentially pullback attracts all solutions starting from a tempered random set. When the non-autonomous deterministic forcings are time-periodic, we obtain the existence, uniqueness and exponential stability of pathwise random periodic solutions for the stochastic lattice systems with delay. The convergence of the tempered complete quasi-solution (periodic solution) is also established when time delay approaches zero.