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Stochastic Analysis of the Fractional Brownian Motion

Stochastic Analysis of the Fractional Brownian Motion Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô–Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Potential Analysis Springer Journals

Stochastic Analysis of the Fractional Brownian Motion

Potential Analysis , Volume 10 (2) – Sep 30, 2004

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Mathematics; Functional Analysis; Potential Theory; Geometry; Probability Theory and Stochastic Processes
ISSN
0926-2601
eISSN
1572-929X
DOI
10.1023/A:1008634027843
Publisher site
See Article on Publisher Site

Abstract

Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô–Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

Journal

Potential AnalysisSpringer Journals

Published: Sep 30, 2004

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