A generalized Fernique theorem and applications
Probability
2010-04-14 v2 Functional Analysis
Abstract
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 H\"older norms of the (fractional) Brownian rough path, Gaussian rough paths and the Banach space valued Wiener process enhanced with its L\'evy area [Ledoux, Lyons, Quian. "L\'evy area of Wiener processes in Banach spaces". Ann. Probab., 30(2):546--578, 2002] then all follow from applying our main theorem.
Cite
@article{arxiv.1004.1923,
title = {A generalized Fernique theorem and applications},
author = {Peter Friz and Harald Oberhauser},
journal= {arXiv preprint arXiv:1004.1923},
year = {2010}
}
Comments
To be published in the Proceedings of the AMS.