Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations

In this paper, we introduce a new concept of Stepanov-like almost automorphy (orS2S2-almost automorphy) for stochastic processes. We use the results obtained to investigate the existence and uniqueness of a Stepanov-like almost automorphic mild solution to a class of nonlinear stochastic differential equations in a real separable Hilbert space. Our main results extend some known ones in the sense of square-mean almost automorphy.