Generalized Backward doubly SDEs driven by L\'evy processes with discontinuous and linear growth coefficients

TL;DR

This paper studies generalized backward doubly stochastic differential equations driven by Lévy processes, establishing the existence of minimal and maximal solutions under certain continuity and growth conditions.

Contribution

It introduces new existence results for solutions of GBDSDEL with discontinuous and linearly growing coefficients driven by Lévy processes.

Findings

Existence of minimal solutions under linear growth conditions

Existence of maximal solutions under linear growth conditions

Applicable to equations with discontinuous coefficients

Abstract

This paper deals with generalized backward doubly stochastic differential equations driven by a L\'evy process (GBDSDEL, in short). Under left or right continuous and linear growth conditions, we prove the existence of minimal (resp. maximal) solutions.