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.
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Decreusefond, L., üstünel, A. Stochastic Analysis of the Fractional Brownian Motion. Potential Analysis 10, 177–214 (1999). https://doi.org/10.1023/A:1008634027843
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DOI: https://doi.org/10.1023/A:1008634027843