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Zbl 1211.60025
Chang, Yong-Kui; Zhao, Zhi-Han; N'guérékata, G.M.
Square-mean almost automorphic mild solutions to non-autonomous stochastic differential equations in Hilbert spaces. (English)
[J] Comput. Math. Appl. 61, No. 2, 384-391 (2011). ISSN 0898-1221

Summary: We first refine the definition of square-mean almost automorphic functions introduced by {\it M. Fu} and {\it Zh. Liu} [Proc. Am. Math. Soc. 138, No. 10, 3689--3701 (2010; Zbl 1202.60109)], then we prove the existence and uniqueness of square-mean almost automorphic mild solutions for a class of non-autonomous stochastic differential equations in a real separable Hilbert space. Some additional properties of square-mean almost automorphic functions are also provided. To prove our main result, we use the Banach contraction mapping principle.

MSC 2000:: *60H25 Random operators, etc.
60H10 Stochastic ordinary differential equations
34C27 Almost periodic solutions of ODE

Keywords: non-autonomous stochastic differential equations; stochastic processes; square-mean almost automorphic; evolution system

Citations: Zbl 1202.60109

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