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Square-mean almost automorphic mild solutions to non-autonomous stochastic differential equations in Hilbert spaces. (English) Zbl 1211.60025
Summary: We first refine the definition of square-mean almost automorphic functions introduced by M. Fu and 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:
60H25 Random operators and equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
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