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

被引：26

作者：

EINMAHL, U

机构：

来源：

ANNALS OF PROBABILITY | 1993年 / 21卷 / 04期

关键词：

BOUNDED LAW OF THE ITERATED LOGARITHM; K-FUNCTION; LIL BEHAVIOR; RANDOMIZATION; RADEMACHER RANDOM VARIABLES;

D O I：

10.1214/aop/1176989009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：2012 / 2045

页数：34

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