# Reflected Discontinuous Backward Doubly Stochastic Differential Equation With Poisson Jumps

## TL;DR

This paper establishes the existence and comparison theorems for reflected backward doubly stochastic differential equations with Poisson jumps, including solutions with continuous barriers and linear growth conditions.

## Contribution

It introduces new existence results and a comparison theorem for RBDSDEPs with Poisson jumps, expanding the theoretical understanding of these stochastic equations.

## Key findings

- Existence of solutions for RBDSDEPs with continuous barriers.
- Comparison theorem for minimal and maximal solutions.
- Solutions under linear growth and left continuity conditions.

## Abstract

In this paper{\}we prove the existence of a solution for reflected backward doubly stochastic differential equations with poisson jumps (RBDSDEPs) with one continuous barrier where the generator is continuous and also we study the RBDSDEPs with a linear growth condition and left continuity in $y$ on the generator. By a comparison theorem established here for this type of equation we provide a minimal or a maximal solution to RBDSDEPs.