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


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 PDE Forward backward stochastic differential equations Skorokhod problem Reflected Stochastic Differential Equations 

AMS subject classifications

60H10 35K55 60J60 60K25 

Copyright information

© Sociedad Española de Matemática Aplicada 2010

Authors and Affiliations

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

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