Large deviations for rough paths of the fractional Brownian motion
Probability
2007-05-23 v1
Abstract
Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths, extending classical results on Gaussian processes. As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit integral representation is given.
Keywords
Cite
@article{arxiv.math/0412200,
title = {Large deviations for rough paths of the fractional Brownian motion},
author = {Annie Millet and Marta Sanz-Solé},
journal= {arXiv preprint arXiv:math/0412200},
year = {2007}
}
Comments
32 pages