@article{EJP2467,
author = {Khaled Bahlali and Lucian Maticiuc and Adrian Zalinescu},
title = {Penalization method for a nonlinear Neumann PDE via weak solutions of reflected SDEs},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {Reflecting stochastic differential equation; Penalization method; Weak solution; Jakubowski S-topology; Backward stochastic differential equations},
abstract = {In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on a penalization method and our approach is probabilistic. We prove the weak uniqueness of the solution for the reflected stochastic differential equation and we approximate it (in law) by a sequence of solutions of stochastic differential equations with penalized terms. Using then a suitable generalized backward stochastic differential equation and the uniqueness of the reflected stochastic differential equation, we prove the existence of a continuous function, given by a probabilistic representation, which is a viscosity solution of the considered partial differential equation. In addition, this solution is approximated by the penalized partial differential equation.},
pages = {no. 102, 1-19},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2467},
url = {http://ejp.ejpecp.org/article/view/2467}}