Limiting behavior of invariant measures for stochastic delay nonlocallattice dynamical systems

Abstract

This paper deals with the limiting behavior of invariant measures of the stochastic delay lattice systems with fractional discrete Laplacian driven by nonlinear noise. Under certain conditions, we first show the existence of invariant measures of the systems. We then prove that any limit point of a tight sequence of invariant measures of the stochastic delay lattice systems with fractional discrete Laplacian must be an invariant measure of the corresponding limiting system as the intensity of noise converges or the time-delay approaches zero.