$B^p$-almost periodic solutions in finite-dimensional distributions to semilinear stochastic differential equations

Abstract

In this paper, we consider a class of semilinear stochastic differential equations in real separable Hilbert spaces. Based on the theory of evolutionary operator family, Banach fixed point theorem and inequality technique, we obtain the existence and uniqueness of $p$-th Besicovitch almost periodic ($B^p$-almost periodic) solutions in finite-dimensional distributions  of this class of semilinear stochastic differential equations. Finally, we provide an example to demonstrate the effectiveness of our results.