Local time and Tanaka formula for G-Brownian Motion
Qian Lin
TL;DR
This paper extends the concepts of local time and Tanaka formula to G-Brownian motion, establishing joint continuity, quadratic variation, and a generalized Itô's formula for convex functions.
Contribution
It introduces the notion of local time and Tanaka formula for G-Brownian motion, along with joint continuity and a generalized Itô's formula, advancing stochastic calculus under model uncertainty.
Findings
Established joint continuity of local time
Proved quadratic variation of G-Brownian motion
Generalized Itô's formula for convex functions
Abstract
In this paper, we study the notion of local time and 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 It^o's formula with respect to the G-Brownian motion to convex functions.
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