Reflected Generalized Backward Doubly SDEs driven by Lévy processes and Applications

Details Reflected Generalized Backward Doubly SDEs driven by Lévy processes and Applications Reflected Generalized Backward Doubly SDEs driven by Lévy processes and Applications

2010-11-12

arxiv.org/abs/1011.3025v1

Mathematics

Probability

18 pages; accepted for publication to journal of theoretical probability

Scientific paper

In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with L\'evy process (RGBDSDELs, in short) with one continuous barrier. Under uniformly Lipschitz coefficients, we prove 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.

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