Properties of solutions of stochastic differential equations driven by the G-Brownian motion

TL;DR

This paper investigates the differentiability and stability of solutions to stochastic differential equations driven by G-Brownian motion, providing insights into their behavior with respect to initial data and parameters.

Contribution

It introduces new results on the differentiability and stability of SDE solutions under G-Brownian motion, extending classical theory to this nonlinear setting.

Findings

Solutions are differentiable with respect to initial data and parameters.

Stability properties of solutions are established under G-Brownian motion.

Results extend classical stochastic calculus to the G-framework.

Abstract

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained.