Existence of almost automorphic solution in distribution for a class of stochastic integro-differential equation driven by Lévy noise

Abstract

We investigate a class of stochastic integro-differential equations driven by Lévy noise. Under some appropriate assumptions, we establish the existence of a square-mean almost automorphic solution in distribution. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution in distribution is obtained by using the condition which is weaker than Lipschitz conditions. We provide an example to illustrate ours results.