Weak mean attractor and periodic measure for stochastic lattice systems driven by Lévy noises

Abstract This work is devoted to stochastic reaction-diffusion lattice system driven by Lévy noises when the drift and diffusion terms are locally Lipschitz continuous. First, we investigate the existence and uniqueness of solutions of such system as well as weak pullback mean random attractors. Then the existence of periodic measures is obtained by the idea of uniform tail-estimates and Krylov-Bogolyubov’s method. Under further conditions, we establish the uniqueness and the exponentially mixing property of periodic measure. Finally, the limit behavior of periodic measures is investigated for stochastic lattice system driven by Lévy noises with respect to noise intensities.