An averaging principle for nonlinear parabolic PDEs via reflected FBSDEs driven by G-Brownian motion

Abstract

In this paper, we are concerned with the averaging problem for a class of forward-backward stochastic differential equations with reflection driven by G-Brownian motion (reflected G-FBSDEs), which corresponds to the singular perturbation problem of a kind of fully nonlinear partial differential equations (PDEs) with a lower obstacle. The reflection keeps the solution above a given stochastic process. By the use of the nonlinear stochastic techniques and viscosity solution methods, we prove that the limit distribution of solution is the unique viscosity solution of an obstacle problem for a fully nonlinear parabolic PDEs.