Multivalued backward doubly stochastic differential equations with time delayed coefficients

TL;DR

This paper studies a class of complex stochastic differential equations with multiple solutions and time delays, extending existing theories to establish existence and uniqueness of solutions using Yosida approximation.

Contribution

It introduces a novel approach to handle multivalued backward doubly stochastic differential equations with time delays, expanding the theoretical framework.

Findings

Established existence and uniqueness of solutions

Extended the theory to multivalued equations with delays

Utilized Yosida approximation for proofs

Abstract

In this paper, we deal with a class of multivalued backward doubly stochastic differential equations with time delayed coefficients. Based on a slight extension of the existence and uniqueness of solutions for backward doubly stochastic differential equations with time delayed coefficients, we establish the existence and uniqueness of solutions for these equations by means of Yosida approximation.