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Stochastic PDIEs with nonlinear Neumann boundary conditions and generalized backward doubly stochastic differential equations driven by Lévy processes. (English) Zbl 1173.60023

A new class of generalized backward doubly stochastic differential equations driven by Teugels martingales associated with Levy process and the integral with respect to an adapted continuous increasinig process is investigated. The existence and uniqueness of solutions to these equations are considered. A probabilistic interpretation for solutions to a class of stochastic partial differential equations with a nonlinear Neumann boundary is given.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60H05 Stochastic integrals
34F05 Ordinary differential equations and systems with randomness
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