Backward doubly stochastic differential equations with weak assumptions on the coefficients

TL;DR

This paper studies one-dimensional backward doubly stochastic differential equations with weak conditions on coefficients, establishing generalized theorems for existence and comparison under less restrictive assumptions.

Contribution

It introduces generalized existence and comparison theorems for BDSDEs with coefficients that are only left Lipschitz and uniformly continuous, relaxing previous assumptions.

Findings

Established a generalized comparison theorem for BDSDEs.

Proved a generalized existence theorem under weak coefficient conditions.

Extended the theory of BDSDEs to more general coefficient functions.

Abstract

In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs) where the coefficient is left Lipschitz in y (may be discontinuous) and uniformly continuous in z. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs .