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

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

2003-04-30

arxiv.org/abs/math/0304501v2

Mathematics

Probability

Scientific paper

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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