Generalized backward doubly stochastic differential equations driven by L\'evy processes with continuous coefficients

TL;DR

This paper introduces a new class of generalized backward doubly stochastic differential equations driven by Lévy processes, establishing key theoretical results including a comparison theorem and existence of solutions under specific conditions.

Contribution

It extends the theory of backward doubly stochastic differential equations to include Lévy processes and provides foundational results for their solvability.

Findings

Established a comparison theorem for GBDSDEs driven by Lévy processes.

Proved existence of solutions under continuous and linear growth conditions.

Extended stochastic differential equation theory to include Lévy-driven processes.

Abstract

A new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with L\'evy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.