Reflected generalized backward doubly SDEs driven by L\'evy processes and Applications

TL;DR

This paper studies a new class of reflected generalized backward doubly stochastic differential equations driven by Lévy processes, establishing existence, uniqueness, and linking solutions to nonlinear PDEs with boundary conditions.

Contribution

It introduces and analyzes reflected GBDSDEs driven by Lévy processes, providing existence, uniqueness, and a probabilistic interpretation for related PDEs.

Findings

Existence and uniqueness of solutions to reflected GBDSDEs

Probabilistic representation of solutions to nonlinear PDEs with boundary conditions

Connection between stochastic differential equations and partial differential integral equations

Abstract

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with L\'{e}vy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of reflected stochastic partial differential integral equations (PDIEs in short) with a nonlinear Neumann boundary condition is given.