$L^p$-solutions of Reflected Backward Doubly Stochastic Differential Equations

TL;DR

This paper establishes the existence and uniqueness of solutions for a specific class of reflected backward doubly stochastic differential equations with Lipschitz coefficients, advancing the theoretical understanding of such stochastic systems.

Contribution

It introduces new results on the existence and uniqueness of solutions for reflected backward doubly stochastic differential equations with a continuous lower barrier.

Findings

Proved existence of solutions under Lipschitz conditions.

Established uniqueness of solutions for the class of equations.

Extended theoretical framework for reflected backward doubly stochastic differential equations.

Abstract

In this paper, we deal with a class of one-dimensional reflected backward doubly stochastic differential equations with one continuous lower barrier. We derive the existence and uniqueness of solutions for these equations with Lipschitz coefficients.