Reflected Generalized Backward Doubly SDEs Driven by Lévy Processes and Applications

Auguste Aman ()
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Auguste Aman: Université de Cocody

Journal of Theoretical Probability, 2012, vol. 25, issue 4, 1153-1172

Abstract: 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.

Keywords: Reflected backward doubly SDEs; Stochastic PDIEs; Lévy process; Teugels martingale; Neumann boundary condition; 60H15; 60H20 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-010-0328-1

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