INVARIANT MEASURES AND LIMIT BEHAVIOR FOR SEMI-LINEAR NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EVOLUTION EQUATIONS WITH INFINITE DELAY

This paper studies the existence and limit behavior of invariant measures for a class of semi-linear neutral stochastic integro-differential evolution equations with infinite delay in Hilbert space driven by Lévy processes. First, the existence and essential properties of fundamental solution of the corresponding linear equation of the considered equation are established, which enables us to represent mild solutions of this equation by fundamental solution through the Laplace transformation method. Then, the existence of global mild solutions is proved by applying Banach fixed point principle. Based on this the existence, uniqueness and limit behavior of invariant measures associated with this equation are respectively discussed by utilizing the theory of resolvent operators and stochastic processes. Finally, an illustrative example is provided to demonstrate the applications of the obtained results.