A generalized Fernique theorem and applications

Friz, Peter; Oberhauser, Harald

doi:10.1090/S0002-9939-2010-10528-2

A generalized Fernique theorem and applications
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by Peter Friz and Harald Oberhauser

Proc. Amer. Math. Soc. 138 (2010), 3679-3688

DOI: https://doi.org/10.1090/S0002-9939-2010-10528-2

Published electronically: June 15, 2010

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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 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, Qian. “Lévy area of Wiener processes in Banach spaces”, Ann. Probab., 30(2):546–578, 2002] then all follow from applying our main theorem.

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