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Potential Analysis

, Volume 10, Issue 2, pp 177–214 | Cite as

Stochastic Analysis of the Fractional Brownian Motion

  • L. Decreusefond
  • A.S. üstünel
Article

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.

Fractional Brownian motion stochastic calculus of variations Itô formula Girsanov Formula. 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • L. Decreusefond
    • 1
  • A.S. üstünel
    • 1
  1. 1.École Nationale Supérieure des TélécommunicationsParisFrance. E-mail

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