Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

TL;DR

This paper establishes existence and uniqueness results for irregular barrier reflected backward doubly stochastic differential equations driven by Brownian motions and Poisson jumps, under stochastic Lipschitz and linear growth conditions.

Contribution

It extends the theory of reflected BDSDEs to irregular barriers and general jumps, relaxing growth conditions on coefficients.

Findings

Proved existence and uniqueness under stochastic Lipschitz conditions.

Extended results to irregular barriers not necessarily right-continuous.

Relaxed growth conditions on coefficients for broader applicability.

Abstract

In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.