Square-mean pseudo almost automorphic process and its application to stochastic evolution equations

This paper introduces the concept of the square-mean pseudo almost automorphy for a stochastic process. Also it introduces the properties on the completeness and the composition of the space that consists of such processes. With appropriate settings and by virtue of the theory of the semigroups of the operators to an evolution family, the Banach fixed point theorem and the stochastic analysis techniques, this paper investigates the existence, the uniqueness and the global stability of the square-mean pseudo almost automorphic solutions for a general class of stochastic evolution equations. Finally, this paper provides an illustrative example to justify the practical usefulness of the established theoretical results.