科研之友
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摘要
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 Holder norms of the (fractional) Brownian rough path, Gaussian rough paths and the Banach space valued Wiener process enhanced with its Levy area [Ledoux, Lyons, Qian. "Levy area of Wiener processes in Banach spaces", Ann. Probab., 30(2):546-578, 2002] then all follow from applying our main theorem.
- 出版日期2010-10
