An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion

Abstract

An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in $(\mathrm{1}/\mathrm{2},\mathrm{1})$ is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.