Asymptotic Dynamics of Stochastic Lattice Differential Equations: A Review

Abstract

This is an expository article on asymptotic dynamics of stochastic lattice differential equations. In particular, we investigate the long-term behavior of stochastic lattice differential equations, by using the concept of global random pullback attractor in the framework of random dynamical systems. General results on the existence of global compact random attractors are first provided for general random dynamical systems in weighted spaces of infinite sequences. They are then used to study the existence of global pullback random attractors for various types of stochastic lattice dynamical systems with white noise.