Dynamics of stochastic reaction diffusion lattice systems driven by nonlinear noise

This paper is concerned with the dynamics of the stochastic reaction diffusion lattice systems defined on the entire integer set driven by locally Lipschitz nonlinear noise. We prove the existence and uniqueness of solutions as well as weak pullback random attractors for the mean random dynamical systems generated by the solution operators. The existence of invariant measures in 2 for the stochastic equations is also established. The idea of uniform estimates on the tails of the solutions is employed to show the tightness of a family of probability distributions of the solutions. (C) 2019 Elsevier Inc. All rights reserved.