Wellposedness and averaging principle for conditional distribution dependent SDEs driven by standard Brownian motions and fractional Brownian motions

Abstract

In this paper, we study a conditional distribution dependent stochastic differential equations driven by standard Brownian motion and fractional Brownian motion with Hurst exponent $H>\frac{1}{2}$ simultaneously. First, the existence and uniqueness of the equation is established by the fixed point theorem. Then, we show that the solutions of conditional distribution dependent stochastic differential equations can be approximated by the solutions of the associated averaged distribution dependent stochastic differential equations.