Lévy's martingale characterization and reflection principle of $G$-Brownian motion

Abstract

In this paper, we obtain Lévy'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.

References in corpus (1)

• Nonlinear Expectations and Stochastic Calculus under Uncertainty

Cited by in corpus (2)

• Functional central limit theorems for random vectors under sub-linear expectations
• Local time and Tanaka formula of $G$-martingales