The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs

TL;DR

This paper establishes that for backward doubly stochastic differential equations with continuous linear growth coefficients, the properties of solution uniqueness and continuous dependence on data are mathematically equivalent.

Contribution

It proves the equivalence between solution uniqueness and continuous dependence for BDSDEs under specific regularity conditions.

Findings

Uniqueness and continuous dependence are equivalent for BDSDEs with continuous linear growth coefficients.

The result links solution stability to uniqueness, aiding in the analysis of BDSDEs.

Provides theoretical foundation for the stability analysis of solutions to BDSDEs.

Abstract

In this paper, we prove that, if the coefficient f = f(t; y; z) of backward doubly stochastic differential equations (BDSDEs for short) is assumed to be continuous and linear growth in (y; z); then the uniqueness of solution and continuous dependence with respect to the coefficients f, g and the terminal value are equivalent.