TOWARD A GENERAL LAW OF THE ITERATED LOGARITHM IN BANACH-SPACE

• 成果类型: Article
• 署名作者: EINMAHL, U
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989009
• 发表日期: 1993
• 页码: 2012-2045
• 关键词: valued random-variables; independent random-variables; exponential inequalities; LIMIT-THEOREMS; sure behavior; universal law; gaussian law; partial-sums; attraction; domain

摘要

A general bounded law of the iterated logarithm for Banach space valued random variables is established. Our result implies: (a) the bounded LIL of Ledoux and Talagrand, (b) a bounded LIL for random variables in the domain of attraction of a Gaussian law and (c) new LIL results for random variables outside the domain of attraction of a Gaussian law in cases where the classical norming sequence {root nLLn} does not work. Basic ingredients of our proof are an infinite-dimensional Fuk-Nagaev type inequality and an infinite-dimensional version of Klass's K-function.