A generalized Fernique theorem and applications

Authors:
Peter Friz and Harald Oberhauser

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

MSC (2010):
Primary 60G15, 60H99; Secondary 60B99

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

Published electronically:
June 15, 2010

MathSciNet review:
2661566

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Peter Friz**

Affiliation:
Institut für Mathematik, Technical University of Berlin, D-10623 Berlin, Germany – and – Weierstrass Institut for Angewandte Analysis and Stochastik, Berlin, Germany

Email:
friz@math.tu-berlin.de

**Harald Oberhauser**

Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, England

Email:
h.oberhauser@statslab.cam.ac.uk

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

Received by editor(s):
September 29, 2009

Published electronically:
June 15, 2010

Additional Notes:
The second author was supported by EPSCR Grant EP/P502365/1 and a DOC-fellowship of the Austrian Academy of Sciences

Communicated by:
Peter A. Clarkson

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.