Integrability of Seminorms

Details Integrability of Seminorms Integrability of Seminorms

2009-09-10

arxiv.org/abs/0909.1895v1

Mathematics

Probability

18 pages

Scientific paper

We study integrability and equivalence of L^p-norms of polynomial chaos elements. Relying on known results for Banach space valued polynomials, a simple technique is presented to obtain integrability results for random elements that are not necessarily limits of Banach space valued polynomials. This enables us to prove integrability results for a large class of seminorms of stochastic processes and to answer, partially, a question raised by C. Borell (1979, Seminaire de Probabilites, XIII, 1-3).

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