English

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 H]1/4,1/2[H\in]{1/4}, {1/2}[ 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