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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: June 15, 2010
MathSciNet review: 2661566
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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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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: http://dx.doi.org/10.1090/S0002-9939-2010-10528-2
PII: S 0002-9939(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.