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Almost periodic solutions and stable solutions for stochastic differential equations

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    * Corresponding author

The first author is supported by National Research Program of China Grant 2013CB834100, Jilin DRC Grant 2017C028-1, NSFC Grants 11571065 and 11171132; the second author is supported by NSFC Grants 11522104 and 11871132, and the startup and Xinghai Jieqing funds from Dalian University of Technology

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  • In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov functions. Under suitable conditions besides Lyapunov functions, we obtain the existence of almost periodic solutions in distribution.

    Mathematics Subject Classification: Primary: 60H10, 34C27; Secondary: 37B25.


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