Large deviations for rough paths of the fractional Brownian motion

Details Large deviations for rough paths of the fractional Brownian motion Large deviations for rough paths of the fractional Brownian motion

2004-12-09

arxiv.org/abs/math/0412200v1

Mathematics

Probability

32 pages

Scientific paper

10.1016/j.anihpb.2005.04.003

Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ 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.

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