Invariant measures for stochastic delay nonlocal lattice dynamical systems

This paper deals with the dynamics of the stochastic delay lattice systems with fractional discrete Laplacian driven by nonlinear noise. The existence of a invariant measure for the stochastic delay nonlocal lattice systems is established under certain conditions. The idea of the uniform estimates on the tails of the solutions, the technique of diadic division and the ArzelaAscoli theorem are employed to show the tightness of a family of probability distributions of the solutions.