Large deviations for rough paths of the fractional Brownian motion
arXiv:math/0412200 · doi:10.1016/j.anihpb.2005.04.003
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.
32 pages