Reflected backward doubly stochastic differential equations with discontinuous generator

TL;DR

This paper investigates one-dimensional reflected backward doubly stochastic differential equations with discontinuous generators, establishing a comparison theorem and identifying minimal and maximal solutions.

Contribution

It introduces a comparison theorem for RBDSDEs with discontinuous generators and characterizes extremal solutions, advancing the theoretical understanding of these equations.

Findings

Established a comparison theorem for RBDSDEs with discontinuous generators

Identified minimal and maximal solutions for these equations

Extended the theory of RBDSDEs to include discontinuous generators

Abstract

In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a comparison theorem establish here for RBDSDEs, we provide a minimal or a maximal solution to RBDSDEs