New Results on Pseudo Almost Automorphic Solutions in Distribution to a Mean Field Stochastic Differential Equation Driven by Fractional Brownian Motion

This paper first presents a new definition of pseudo almost automorphic stochastic processes in distribution, and then applies inequality techniques and Banach fixed point theorem to establish the existence and global exponential stability of pseudo almost automorphic solutions in distribution for a class of mean field stochastic differential equations driven by Brownian and fractional Brownian motions. The results and methods presented in this paper are both novel.