Local time and Tanaka formula for the G-Brownian motion

摘要

In this paper, we study the notion of local time and obtain the Tanaka formula for the G-Brownian motion. Moreover, the joint continuity of the local time of the G-Brownian motion is obtained and its quadratic variation is proven. As an application, we generalize the It? formula with respect to the G-Brownian motion to convex functions.