Some sample path properties of G-Brownian motion

TL;DR

This paper investigates fundamental path properties of G-Brownian motion, including zero set characterization, local maxima, and integrability of indicator functions, advancing the understanding of G-expectation theory.

Contribution

It provides new insights into the absolute path properties of G-Brownian motion, particularly regarding zero sets, local maxima, and the integrability of indicator functions.

Findings

Characterization of the zero set of G-Brownian motion

Identification of local maxima properties

Proof that indicator functions are in _G^1(Omega)

Abstract

In this paper, we shall study the basic absolute properties of $G$-Brownian motion, i.e., those properties which hold for q.s. $\omega$. These include the characterization of the zero set and the local maxima of the $G$-Brownian motion paths. We also show that the indicator function of $G$-Brownian motion is in $\mathbb{L}_G^1(\Omega)$, which is an useful tool for the study of $G$-expectation theory.