An approximation result for a nonlinear Neumann boundary value problem via BSDEs

Abstract

We prove a weak convergence result for a sequence of backward stochastic differential equations related to a semilinear parabolic partial differential equation; under the assumption that the diffusion corresponding to the PDEs is obtained by penalization method converging to a normal reflected diffusion on a smooth and bounded domain D. As a consequence we give an approximation result to the solution of semilinear parabolic partial differential equations with nonlinear Neumann boundary conditions. A similar result in the linear case was obtained by Lions et al. in 1981.