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

Abstract In this paper, we introduce a new concept of Stepanov-like almost automorphy (or S 2 -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.

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