Existence and global attractiveness of a square-mean μ-pseudo almost automorphic solution for some stochastic evolution equation driven by Lévy noise

Abstract

In this work, we introduce the concept of μ-pseudo almost automorphic processes in distribution. We use the μ-ergodic process to define the spaces of μ-pseudo almost automorphic processes in the square mean sense. We establish many interesting results on the functional space of such processes like a composition theorem. Under some appropriate assumptions, we establish the existence, the uniqueness and the stability of the square-mean μ-pseudo almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Levy noise. We provide an example to illustrate our results.