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October 20, 2025Open Access

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

Key Points

Existence and uniqueness of solutions are proven for reflected generalized backward doubly stochastic differential equations.
A probabilistic representation is derived for viscosity solutions related to an obstacle problem governed by stochastic integro-PDEs.
The study applies stochastic conditions on coefficients to derive key results in the context of Lévy processes.
The findings enhance understanding of how nonlinear Neumann boundary conditions affect stochastic integro-PDE systems.

Abstract

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous Lévy 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.

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

Key Points

Abstract

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