BSDEs driven by G-Brownian motion with time-varying uniformly continuous generators

TL;DR

This paper investigates G-BSDEs driven by G-Brownian motion with generators that are time-varying Lipschitz and uniformly continuous, establishing existence, uniqueness, and comparison results using approximation and G-stochastic analysis techniques.

Contribution

It introduces a novel approach to handle time-varying generators in G-BSDEs, extending existing theory to more general conditions.

Findings

Proved existence and uniqueness of solutions under new conditions.

Established a comparison theorem for G-BSDEs with time-varying generators.

Developed approximation methods and a priori estimates for G-BSDEs.

Abstract

In this paper, we study the backward stochastic differential equations driven by G-Brownian motion under the condition that the generator is time-varying Lipschitz continuous with respect to y and time-varying uniformly continuous with respect to z. With the help of linearization method and the G-stochastic analysis techniques, we construct the approximating sequences of G-BSDE and obtain some precise a priori estimates. By combining this with the approximation method, we prove the existence and uniqueness of the solution under the time-varying conditions, as well as the comparison theorem.