Some sample path properties of G-Brownian motion

2014/07/01 by Falei Wang, Wang, Falei, Guoqiang Zheng +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.0211

openalex publication_date 2014/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we shall study the basic absolute properties of G-Brownian motion, i.e., those properties which hold for q.s. ω. 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 \mathbbL_G¹(Ω), which is an useful tool for the study of G-expectation theory.

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