Stochastic analysis of the fractional Brownian motion. (English) Zbl 0924.60034

Since the fractional Brownian motion (fBm) is not a semimartingale, the usual stochastic calculus cannot be used to analyze it; however since it is a Gaussian process, the authors have applied the stochastic calculus of variations which is valid on general Wiener spaces. By using some well-known properties of the standard Brownian motion, the authors obtain the Itô-Clark representation formula. By an intrinsic analysis of the fBm, they obtain the Itô formula and the Girsanov theorem. Throughout the paper, they give two practical applications such as the simulation of sample-paths of the fBm and an estimation problem involving an fBm.


60H07 Stochastic calculus of variations and the Malliavin calculus
60G18 Self-similar stochastic processes
Full Text: DOI