Stochastic Analysis of the Fractional Brownian Motion

摘要

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