Existence and asymptotic stability for lattice stochastic integrodifferential equations with infinite delays

Abstract

We prove a new result of resolvent operators generated by the lattice operator, and investigate the existence and asymptotic stability of mild solutions for a class of lattice stochastic integrodifferential equations with infinite delays driven by fractional Brownian motion. With the help of the Banach fixed point theorem and some inequality techniques, the existence of mild solutions are obtained. We give some sufficient conditions to ensure the asymptotic stability of mild solutions in the mean square moment.