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Zbl 1217.60043
Chang, Yong-Kui; Zhao, Zhi-Han; N'Guérékata, G.M.
A new composition theorem for square-mean almost automorphic functions and applications to stochastic differential equations. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2210-2219 (2011). ISSN 0362-546X

Summary: We establish a new composition theorem for square-mean almost automorphic functions under conditions which are different from Lipschitz conditions in the literature. We apply this new composition theorem together with Schauder's fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions for a stochastic differential equation in a real separable Hilbert space. Finally, an interesting corollary is given for the sub-linear growth cases.

MSC 2000:: *60H10 Stochastic ordinary differential equations
35B15 Almost periodic solutions of PDE

Keywords: composition theorem of square-mean almost automorphic functions; stochastic differential equations; Schauder's fixed point theorem

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