Integrability of Seminorms

摘要

We study integrability and equivalence of $L^p$-norms of polynomial chaos elements. Relying on known results for Banach space valued polynomials, we extend and unify integrability for seminorms results to 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).