Symmetrization and concentration inequalities for multilinear forms with applications to zero-one laws for Levy chaos

• 成果类型: Article
• 署名作者: Rosinski, J; Samorodnitsky, G
• 署名单位: Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 422-437
• 关键词: representations

摘要

We consider stochastic processes X = {X(t), t is an element of T} represented as a Levy chaos of finite order, that is, as a finite sum of multiple stochastic integrals with respect to a symmetric infinitely divisible random measure. For a measurable subspace V of RT We prove a very general zero-one law P(X is an element of V) = 0 or 1, providing a complete analog to the corresponding situation in the case of symmetric infinitely divisible processes (single integrals with respect to an infinitely divisible random measure). Our argument requires developing a new symmetrization technique for multilinear Rademacher forms, as well as generalizing Kanter's concentration inequality to multiple sums.