Large deviations for rough paths of the fractional Brownian motion

Annie Millet (1, 2, 3) , Marta Sanz-Solé (4)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CES - Centre d'économie de la Sorbonne
3 SAMOS - Statistique Appliquée et MOdélisation Stochastique
4 Facultat de Matematiques

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.

Mots clés: Rough paths; Large deviation principle; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Annie Millet, Marta Sanz-Solé. Large deviations for rough paths of the fractional Brownian motion. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2006, 42, pp.245-271. ⟨10.1016/j.anihpb.2005.04.003⟩. ⟨hal-00003655⟩