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Zbl 1209.60034
Chang, Yong-Kui; Zhao, Zhi-Han; N'Guérékata, G.M.; Ma, Ruyun
Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 2, 1130-1139 (2011). ISSN 1468-1218

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 2000:: *60H10 Stochastic ordinary differential equations

Keywords: Stepanov-like almost automorphy; square-mean almost automorphy; stochastic differential equations

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