Averaging Principle for Backward Stochastic Differential Equations

Abstract

The averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, is investigated. An averaged BSDEs for the original BSDEs is proposed, as well as the one-barrier RBSDEs, 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 Backward Stochastic Differential Equations driven both standard and fractional Brownian motions

“…Stochastic averaging principle, which is usually used to approximate dynamical systems under random fluctuations, has long and rich history in multiscale problems (see, e.g., [10]). Recently, the averaging principle for BSDEs and one-barrier reflected BSDEs, with Lipschitz coefficients, were first studied by Jing and Li [8]. In the present paper, we study a stochastic averaging technique for a class of the SFrBSDEs (1.1).…”

Averaging Principle for BSDEs and one Barrier Reflected BSDEs With Non-Liphschitz Coefficients

“…Recently, the averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, were first studied by (Jing, Y. & Li, Z.…”

g-Expectation for Conformable Backward Stochastic Differential Equations

“…Recently, Long et al [10] proposed a multi-step scheme on time-space grids for solving backward stochastic differential equations, and Chen and Ye [11] investigated solutions of backward stochastic differential equations in the framework of Riemannian manifold. From the paper [12], we could get the averaging principle for backward stochastic differential equations and the solutions can be approximated by the solutions to averaged stochastic systems in the sense of mean square under some appropriate assumptions.…”