Continuity of the Itô-Map for Holder Rough Paths with Applications to the Support Theorem in Holder Norm View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2005

AUTHORS

Peter K. Friz

ABSTRACT

Rough Path theory is currently formulated in p-variation topology. We show that in the context of Brownian motion, enhanced to a Rough Path, a more natural Holder metric π can be used. Based on fine-estimates in Lyons’ celebrated Universal Limit Theorem we obtain Lipschitz-continuity of the Ito-rnap (between Rough Path spaces equipped with π). We then consider a number of approximations to Brownian Rough Paths and establish their convergence w.r.t. π. In combination with our Holder ULT this allows sharper results than the p-variation theory. Also, our formulation avoids the so-called control functions and may be easier to use for non Rough Path specialists. As concrete application, we combine our results with ideas from [MS] and [LQZ] and obtain the Stroock-Varadhan Support Theorem in Holder topology as immediate corollary. More... »

PAGES

117-135

Book

TITLE

Probability and Partial Differential Equations in Modern Applied Mathematics

ISBN

978-0-387-25879-9
978-0-387-29371-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-0-387-29371-4_8

DOI

http://dx.doi.org/10.1007/978-0-387-29371-4_8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1022676715


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