Almost automorphic solutions for mean-field stochastic differential equations driven by fractional Brownian motion

Abstract

This paper concerns a class of mean field stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. The existence and uniqueness of almost automorphic solutions in distribution of mean field stochastic differential equations driven by fractional Brownian motion are established provided coefficients of equations satisfy some suitable conditions.

Keywords:

• Almost automorphic solutions
• distribution
• mean field stochastic differential equations
• fractional Brownian motion

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 34C27
• 60H10
• 60E05
• 93C30

Acknowledgments

The authors are grateful to the Referee for their careful reading of the first versions of the manuscript which has allowed them to considerably improve the quality of the paper.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant No. 11701077,11801040,11801041) and the project of the Education Department of Jilin Province (Grant No. JJKH20191192KJ)