Stochastic Averaging Principle for Mixed Stochastic Differential Equations

Abstract

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Itô stochastic calculus.