Actas del NSDS09

SeMA Journal

, Volume 51, Issue 1, pp 109-116

First online:

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

  • Pedro Marín-RubioAffiliated withDpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla Email author 
  • , José RealAffiliated withDpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla

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

AMS subject classifications

60H10 35K55 60J60 60K25