Some sample path properties of G-Brownian motion

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.

9 pages, better statements about Theorem 3.5

References in corpus (1)

• On the strict comparison theorem for $G$-expectations

Cited by in corpus (1)

• On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion