Description:
<jats:title>Abstract</jats:title>
<jats:p>In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson
S<jats:sup>2</jats:sup>−almost automorphic) processes in distribution. We establish some interesting results on the functional
space of such processes like an composition theorems. Next, under some suitable assumptions, we establish
the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution
to a class of abstract stochastic evolution equations driven by Lévy noise in case when the functions
forcing are both continuous and S<jats:sup>2</jats:sup>−almost automorphic. We provide an example to illustrate ours results.</jats:p>