L\'{e}vy's martingale characterization and reflection principle of $G$-Brownian motion
Probability
2025-11-25 v1
Abstract
In this paper, we obtain L\'{e}vy's martingale characterization of -Brownian motion without the nondegenerate condition. Base on this characterization, we prove the reflection principle of -Brownian motion. Furthermore, we use Krylov's estimate to get the reflection principle of -Brownian motion.
Keywords
Cite
@article{arxiv.1805.11370,
title = {L\'{e}vy's martingale characterization and reflection principle of $G$-Brownian motion},
author = {Mingshang Hu and Xiaojun Ji and Guomin Liu},
journal= {arXiv preprint arXiv:1805.11370},
year = {2025}
}