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

Abstract

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.

Keywords:

• Averaging principle
• backward stochastic differential equation
• stochastic calculus
• fractional Brownian motion
• Chebyshev's inequality and Itô's representation formula

Mathematic Subjection Classifications::

• 60H05
• 60G44

Disclosure statement

No potential conflict of interest was reported by the author(s).