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Published in:
2006 | OriginalPaper | Chapter
Fractional Brownian motion
Author : David Nualart
Published in: The Malliavin Calculus and Related Topics
Publisher: Springer Berlin Heidelberg
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The fractional Brownian motion is a self-similar centered Gaussian process with stationary increments and variance equals
t
2
H
, where
H
is a parameter in the interval (0, 1). For
H
= ½ this process is a classical Brownian motion. In this chapter we will present the application of the Malliavin Calculus to develop a stochastic calculus with respect to the fractional Brownian motion.