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

2003/04/30 by Peter K. Friz, Friz, Peter K.
Mathematics · #60H99 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H99

paper · pdf · doi:10.48550/arxiv.math/0304501

arxiv created 2003/08/08 · arxiv updated 2009/11/30

Abstract

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.

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