Square-mean almost automorphic mild solutions to non-autonomous stochastic differential equations in Hilbert spaces

In this paper, we first refine the definition of square-mean almost automorphic functions introduced in Fu and Liu (2010) [11], 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.

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