Almost periodic solutions and stable solutions for stochastic differential equations

Yong Li; Zhenxin Liu; Wenhe Wang

doi:10.3934/dcdsb.2019113

Article Contents

2019, Volume 24, Issue 11: 5927-5944. Doi: 10.3934/dcdsb.2019113

This issue Previous Article Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields Next Article Asymptotic behavior of an SIR reaction-diffusion model with a linear source

Almost periodic solutions and stable solutions for stochastic differential equations

1.
School of Mathematics, Jilin University, Changchun 130012, China
2.
Center for Mathematics and Interdisciplinary Sciences, and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
4.
School of Basic Sciences, Changchun University of Technology, Changchun 130012, China

^* Corresponding author
^* Corresponding author

Received: August 31, 2018

Early access: June 2019

Published: August 2019

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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Abstract

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.

Keywords:

Stochastic differential equation,
almost periodic solution,
asymptotically almost periodic solution,
stable in distribution,
Lyapunov function.

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

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References

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