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An approximation result for a nonlinear Neumann boundary value problem via BSDEs

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  • Boufoussi, B.
  • van Casteren, J.

Abstract

We prove a weak convergence result for a sequence of backward stochastic differential equations related to a semilinear parabolic partial differential equation; under the assumption that the diffusion corresponding to the PDEs is obtained by penalization method converging to a normal reflected diffusion on a smooth and bounded domain D. As a consequence we give an approximation result to the solution of semilinear parabolic partial differential equations with nonlinear Neumann boundary conditions. A similar result in the linear case was obtained by Lions et al. in 1981.

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  • Boufoussi, B. & van Casteren, J., 2004. "An approximation result for a nonlinear Neumann boundary value problem via BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 331-350, December.
    • Handle: RePEc:eee:spapps:v:114:y:2004:i:2:p:331-350
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Lejay, Antoine, 2002. "BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogenization," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 1-39, January.
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    Cited by:

    1. Maticiuc, Lucian & Răşcanu, Aurel, 2016. "On the continuity of the probabilistic representation of a semilinear Neumann–Dirichlet problem," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 572-607.
    2. Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2015. "Multivalued backward stochastic differential equations with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3170-3195.

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