A new composition theorem for square-mean almost automorphic functions and applications to stochastic differential equations

In this paper, we establish a new composition theorem for square-mean almost automorphic functions under conditions which are different from Lipschitz conditions in the literature. We apply this new composition theorem together with Schauder’s fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions for a stochastic differential equation in a real separable Hilbert space. Finally, an interesting corollary is also given for the sub-linear growth cases.