Continuity of the Ito-Map for Hoelder rough paths with applications to the support theorem in Hoelder norm

Lyons’ Rough Path theory is currently formulated in p-variation topology. We extend his main-result, the Universal Limit Theorem, to a stronger Hoelder topology. Several approximations to Brownian Rough Paths are studied. As application of our approach, we obtain the celebrated support theorem (in Hoelder-topology) as immediate (!) corollary.