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In this paper, we study the stochastic averaging principle for backward stochastic differential equations driven by two mutually independent fractional Brownian motions (FrBSDEs in short). An averaged FrBSDEs for the original equations 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 in the sense of mean square.

Averaging principle for BSDEs driven by two mutually independent fractional Brownian motions