Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.

RésuméNous etudions les principes de grandes deviations pour les « rough paths Gaussiens », pour une large classe de processus Gaussiens. Cette classe contient le mouvement brownien fractionnaire.