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A generalized Fernique theorem and applications
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Journal Article
A generalized Fernique theorem and applications
2010
Overview
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.
Publisher
American Mathematical Society
Subject
/ Exact sciences and technology
/ General, history and biography
/ Global analysis, analysis on manifolds
/ Numerical analysis in abstract spaces
/ Numerical analysis. Scientific computation
/ Probability theory and stochastic processes
/ Sciences and techniques of general use
/ Tensors
/ Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
