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Reflected Generalized Backward Doubly SDEs Driven by Lévy Processes and Applications

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  • Auguste Aman

    (Université de Cocody)

Abstract

In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with Lévy process (RGBDSDELs in short) with one continuous barrier. Under uniformly Lipschitz coefficients, we prove an existence and uniqueness result by means of the penalization method and the fixed-point theorem. As an application, this study allows us to give a probabilistic representation for the solutions to a class of reflected stochastic partial differential integral equations (SPDIEs in short) with a nonlinear Neumann boundary condition.

Suggested Citation

  • Auguste Aman, 2012. "Reflected Generalized Backward Doubly SDEs Driven by Lévy Processes and Applications," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1153-1172, December.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:4:d:10.1007_s10959-010-0328-1
    DOI: 10.1007/s10959-010-0328-1
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    References listed on IDEAS

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    1. Nualart, David & Schoutens, Wim, 2000. "Chaotic and predictable representations for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 109-122, November.
    2. 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.
    3. Matoussi, Anis, 1997. "Reflected solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 347-354, June.
    4. Mohamed El Otmani, 2006. "Generalized BSDE driven by a Lévy process," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-25, October.
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