Reflected generalized BDSDEs driven by non-homogeneous L\'evy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions

Badr Elmansouri; Mohammed Elhachemy; Mohamed Marzougue; Mohamed El Jamali

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arXiv · 2509.25912

Reflected generalized BDSDEs driven by non-homogeneous L\'evy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions

Badr Elmansouri·Mohammed Elhachemy·Mohamed Marzougue·Mohamed El Jamali

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Abstract

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous L\'evy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution. Furthermore, we apply these results to obtain a probabilistic representation for the viscosity solutions of an obstacle problem governed by stochastic integro-partial differential equations with a nonlinear Neumann boundary condition.

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Badr Elmansouri, Mohammed Elhachemy, Mohamed Marzougue, Mohamed El Jamali. 2025-09-30. Reflected generalized BDSDEs driven by non-homogeneous L\'evy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions. https://arxiv.org/abs/2509.25912

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