A Framework of BSDEs with Stochastic Lipschtz Coefficients through Time Change

TL;DR

This paper introduces a time change technique to analyze backward stochastic differential equations (BSDEs) with stochastic Lipschitz coefficients, establishing their relation to BSDEs with uniform Lipschitz conditions and stopping times.

Contribution

The paper presents a novel method using time change to handle BSDEs with stochastic Lipschitz coefficients, linking them to more tractable BSDEs with uniform Lipschitz properties.

Findings

Established a relation between BSDEs with stochastic and uniform Lipschitz coefficients.

Developed a time change approach to simplify the analysis of BSDEs.

Provided theoretical insights into the structure of BSDEs with stochastic Lipschitz conditions.

Abstract

In this paper, we suggest a useful technique based on time change to be effective for dealing with the backward stochastic differential equations. We show the relation between the BSDEs with stochastic Lipschtz coeffecients and the ones with uniformly Lipschtz coefficients and stopping terminal time.