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Reflected generalized backward doubly SDEs driven by Lévy processes and applications. (English) Zbl 1259.60062
Summary: We study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with Lévy process 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) with a nonlinear Neumann boundary condition.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
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