On the Weighted Local Time and the Tanaka Formula for the Multidimensional Fractional Brownian Motion |
| |
Authors: | Hideaki Uemura |
| |
Institution: | 1. Department of Mathematics Education , Aichi University of Education , Kariya, Japan huemura@auecc.aichi-edu.ac.jp |
| |
Abstract: | Abstract We determine the weighted local time for the multidimensional fractional Brownian motion from the occupation time formula. We also discuss on the Itô and Tanaka formula for the multidimensional fractional Brownian motion. In these formulas the Skorohod integral is applicable if the Hurst parameter of fractional Brownian motion is greater than 1/2. If the Hurst parameter is less than 1/2, then we use the Skorohod type integral introduced by Nualart and Zakai for the stochastic integral and establish the Itô and Tanaka formulas. |
| |
Keywords: | Fractional Brownian motion Itô formula Tanaka formula Skorohod type integral Weighted local time |
|