2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106154We 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 Hoelder- or modulus topology, appears as special case.minor corrections; this version to appear in Annales de l'I.H.PProbability60F10; 60G15; 60H99text