Orlicz norms of sequences of random variables

• 成果类型: Article
• 署名作者: Gordon, Y; Litvak, A; Schütt, C; Werner, E
• 署名单位: Technion Israel Institute of Technology; University of Kiel; University System of Ohio; Case Western Reserve University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 1833-1853
• 关键词: banach-space theory; probabilistic inequalities; Combinatorial

摘要

Let f(i), i = 1, n, be copies of a random variable f and let N be an Orlicz function. We show that for every x is an element of R-n the expectation Eparallel to(x(i)f(i))(i=1)(n)parallel to(N) is maximal (up to an absolute constant) if f(i), i = 1,...,n, are independent. In that case we show that the expectation Eparallel to(x(i) f(i))(i = 1)(n)parallel to(N) is equivalent to parallel toxparallel to(M), for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.