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Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations. (English) Zbl 1209.60034
Summary: 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.
##### MSC:
 60H10 Stochastic ordinary differential equations