Stochastic Calculus with respect to G-Brownian Motion Viewed through Rough Paths

TL;DR

This paper explores the rough path properties of stochastic integrals with respect to G-Brownian motion, providing estimates of its roughness and establishing a Norris lemma within the G-framework.

Contribution

It introduces a novel analysis of G-Brownian motion's rough path properties and derives a pathwise Norris lemma in the G-framework.

Findings

Estimated the roughness of G-Brownian motion.

Established a pathwise Norris lemma in the G-framework.

Analyzed stochastic integrals of Itô and Stratonovich types with respect to G-Brownian motion.

Abstract

In this paper, we study rough path properties of stochastic integrals of It\^{o}'s type and Stratonovich's type with respect to $G$-Brownian motion. The roughness of $G$-Brownian Motion is estimated and then the pathwise Norris lemma in $G$-framework is obtained.