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On the Weighted Local Time and the Tanaka Formula for the Multidimensional Fractional Brownian Motion
Author:
Hideaki Uemura a
| Affiliation: | a Department of Mathematics Education, Aichi University of Education, Kariya, Japan |
DOI:
10.1080/07362990701726365
Publication Frequency:
6 issues per year
Published in:
Stochastic Analysis and Applications,
Volume
26,
Issue
1
January
2008
, pages 136
- 168
Stochastic Analysis and Applications,
Volume
26,
Issue
1
January
2008
, pages 136
- 168
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(English)
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(English)
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Abstract
We determine the weighted local time for the multidimensional fractional Brownian motion from the occupation time formula. We also discuss on the It
 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 It and Tanaka formulas.
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Keywords:
Fractional Brownian motion;
It formula;
Tanaka formula;
Skorohod type integral;
Weighted local time
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| Mathematics Subject Classification: 60H07; 60G15 |
| view references (10) |
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