# American Institute of Mathematical Sciences

April  2018, 38(4): 1935-1953. doi: 10.3934/dcds.2018078

## Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity

 1 School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China 2 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 3 College of Mathematics, Sichuan University, Chengdu, China

* Corresponding author

Received  November 2016 Revised  November 2017 Published  January 2018

Fund Project: Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 11671118). Hailong Zhu was supported by the National NSF of China (NO. 11301001), China Postdoctoral Science Foundation funded project (NO. 2016M591697), NSF of Anhui Province of China(NO. KJ2017A432, NO. 1708085MA17)

In the setting of mean-square exponential dichotomies, we study the existence and uniqueness of mean-square almost automorphic solutions of non-autonomous linear and nonlinear stochastic differential equations.

Citation: Hailong Zhu, Jifeng Chu, Weinian Zhang. Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 1935-1953. doi: 10.3934/dcds.2018078
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