Weyl almost periodic solutions in distribution to a mean-field stochastic differential equation driven by fractional Brownian motion

Abstract

In this paper, we consider a class of mean-field stochastic differential equations driven by both Brownian motion and fractional Brownian motion. Using the Banach fixed point theorem and inequality technique, we obtain sufficient conditions for the existence and uniqueness of Weyl almost periodic solutions in distribution of the equations under consideration.

KEYWORDS:

• Mean-field stochastic differential equation
• Weyl almost periodic solution
• Brownian motion
• fractional Brownian motion

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34C27
• 60H10
• 60E05
• 93C30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 12261098] and the Applied Basic Research Foundation of Yunnan Province [grant number 2019FB003].