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

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 Lévy noise. We provide an example to illustrate our results.