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

In this work, we introduce the concept of mu-pseudo almost automorphic processes in distribution. We use the mu-ergodic process to define the spaces of mu-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 mu-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. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim