SeMA Journal

, Volume 51, Issue 1, pp 109–116

Probabilistic representation of solutions for quasi-linear parabolic PDE via FBSDE with reflecting boundary conditions

Actas del NSDS09

DOI: 10.1007/BF03322561

Cite this article as:
Marín-Rubio, P. & Real, J. SeMA (2010) 51: 109. doi:10.1007/BF03322561

Abstract

A probabilistic representation of the solution (in the viscosity sense) of a quasi-linear parabolic PDE system with non-lipschitz terms and a Neumann boundary condition is given via a fully coupled forward-backward stochastic differential equation with a reflecting term in the forward equation. The extension of previous results consists on the relaxation on the Lipschitz assumption on the drift coefficient of the forward equation, using a previous result of the authors.

Key words

Probabilistic formulae for PDEForward backward stochastic differential equationsSkorokhod problemReflected Stochastic Differential Equations

AMS subject classifications

60H1035K5560J6060K25

Copyright information

© Sociedad Española de Matemática Aplicada 2010

Authors and Affiliations

  1. 1.Dpto. Ecuaciones Diferenciales y Análisis NuméricoUniversidad de SevillaSevillaSpain