English

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 GG-Brownian motion without the nondegenerate condition. Base on this characterization, we prove the reflection principle of GG-Brownian motion. Furthermore, we use Krylov's estimate to get the reflection principle of G~\tilde{G}-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}
}