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arXiv · 1805.11370

L\'{e}vy's martingale characterization and reflection principle of $G$-Brownian motion

Mingshang Hu·Xiaojun Ji·Guomin Liu
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Abstract

In this paper, we obtain L\'{e}vy's martingale characterization of $G$-Brownian motion without the nondegenerate condition. Base on this characterization, we prove the reflection principle of $G$-Brownian motion. Furthermore, we use Krylov's estimate to get the reflection principle of $\tilde{G}$-Brownian motion.

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Mingshang Hu, Xiaojun Ji, Guomin Liu. 2018-05-29. L\'{e}vy's martingale characterization and reflection principle of $G$-Brownian motion. https://doi.org/10.1016/j.jmaa.2019.123436

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