Reflected Generalized Backward Doubly SDEs Driven by Levy Processes and Applications

In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with L,vy 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.