Averaging Principle for BSDEs driven by fractional Brownian motion with non Lipschitz coefficients

Abstract

. Stochastic averaging for a class of backward stochastic differential equations with fractional Brownian motion, of the Hurst parameter H in the interval (cid:0) 12 , 1 (cid:1) , is investigated under the non-Lipschitz condition. An averaged fractional BSDEs for the original fractional BSDEs is proposed, and their solutions are quantitatively compared. Under some appropriate assumptions, the solutions to original systems can be approximated by the solutions to averaged stochastic systems, both in the sense of mean square and also in probability. The stochastic integral used throughout the paper is the divergence-type integral.