Comptes Rendus
no. 1-2
Probability Theory
An approximation result for nonlinear SPDEs with Neumann boundary conditions
[Un résultat d'approximation pour les EDPS avec condition de type Neumann]

Présenté par : Paul Malliavin

Naoual Mrhardy1
1 Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P. 2390 Marrakesh, Morocco
Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 79-82.

Nous établissons un résultat d'approximation pour les équations aux dérivées partielles stochastiques nonlinéaires avec conditions de Neumann. Pour ce faire, nous utilisons la théorie des équations différentielles doublement stochastiques rétrogrades.

We establish an approximation result to the solution of a semi linear stochastic partial differential equation with a Neumann boundary condition. Our approach is based on the theory of backward doubly stochastic differential equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.11.025
Naoual Mrhardy 1

1 Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P. 2390 Marrakesh, Morocco 
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     title = {An approximation result for nonlinear {SPDEs} with {Neumann} boundary conditions},
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Naoual Mrhardy. An approximation result for nonlinear SPDEs with Neumann boundary conditions. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 79-82. doi : 10.1016/j.crma.2007.11.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.025/

[1] B. Boufoussi; J. van Casteren An approximation result for nonlinear Neumann boundary value problem via BSDEs, Stochastic Process. Appl., Volume 114 (2004), pp. 331-350

[2] B. Boufoussi; N. Mrhardy; J. van Casteren Generalized Backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions, Bernoulli, Volume 13 (2007) no. 2, pp. 423-446

[3] R. Buckdahn; J. Ma Stochastic viscosity solutions for nonlinear stochastic PDEs (Part I), Stochastic Process. Appl., Volume 93 (2001), pp. 181-204

[4] P.L. Lions; A.S. Sznitman Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., Volume XXXVII (1984), pp. 511-537

[5] J.L. Menaldi Stochastic variational inequality for reflected diffusion, Indiana Univ. Math. J., Volume 32 (1983) no. 5

[6] E. Pardoux; S. Peng Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Related Fields, Volume 98 (1994), pp. 209-227

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