Square-mean weighted pseudo almost automorphic solutions for non-autonomous stochastic evolution equations

In this paper, we first introduce the concepts and properties of the square-mean weighted pseudo almost automorphy and the square-mean bi-almost automorphy for a stochastic process. With these preliminary settings and by virtue of the theory of the semigroups of the operators, the Banach fixed point theorem and the stochastic analysis techniques, we investigate the well-posedness of the square-mean weighted pseudo almost automorphic solutions for a general class of non-autonomous stochastic evolution equations that satisfy either global or only local Lipschitz condition. Moreover, we estimate the boundedness of attractive domain for the case where the only local Lipschitz condition is taken into account. Finally, we provide two illustrative examples to show the practical usefulness of the analytical results that we establish in the paper.