2010/04/12 by Peter Friz, Friz, Peter, Harald Oberhauser +1 · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR
paper · pdf · doi:10.48550/arxiv.1004.1923
To be published in the Proceedings of the AMS.
arxiv created 2010/04/13 · arxiv updated 2010/04/14
We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated integrals of Gaussian processes (which are generically not Gaussian). Gaussian integrability with explicitly given constants for variation and Hölder norms of the (fractional) Brownian rough path, Gaussian rough paths and the Banach space valued Wiener process enhanced with its Lévy area [Ledoux, Lyons, Quian. "Lévy area of Wiener processes in Banach spaces". Ann. Probab., 30(2):546--578, 2002] then all follow from applying our main theorem.