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
  • 30 Downloads

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Ma and J. Cvitanić, Reflected forward-backward SDEs and obstacle problems with boundary conditions, J. Appl. Math. Stochastic Anal. 14(2) (2001), 113–138.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Vol. 1702 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1999.MATHGoogle Scholar
  3. [3]
    P. Marín-Rubio and J. Real, Some results on stochastic differential equations with reflecting boundary conditions, J. Theoret. Prob. 17(3) (2004), 705–716.MATHCrossRefGoogle Scholar
  4. [4]
    E. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14(1) (1990), 55–61.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    E. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs, Probab. Theory Related Fields 114(2) (1999), 123–150.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    E. Pardoux and S. Zhang, Generalized BSDEs and nonlinear Neumann boundary value problems, Probab. Theory Related Fields 110(4) (1998), 535–558.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Sociedad Española de Matemática Aplicada 2010

Authors and Affiliations

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

Personalised recommendations