ON THE ALMOST SURE BEHAVIOR OF SUMS OF IID RANDOM-VARIABLES IN HILBERT-SPACE

被引：18

作者：

EINMAHL, U

机构：

来源：

ANNALS OF PROBABILITY | 1991年 / 19卷 / 03期

关键词：

LAW OF THE (K-TIMES) ITERATED LOGARITHM; LOWER AND UPPER CLASSES; INTEGRAL TESTS; COMPACT AND BOUNDED COVARIANCE OPERATORS; GAUSSIAN RANDOM VARIABLES IN HILBERT SPACE;

D O I：

10.1214/aop/1176990342

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：

We study the almost sure behavior of sums of iid random variables satisfying the bounded LIL in Hilbert space. We show that the almost sure behavior is different from the Gaussian case, whenever the second strong moments are infinite. A law of the kappa times iterated logarithm is established which refines the bounded LIL. The interesting feature here is that contrary to the known conditions for the bounded LIL, one needs not only moment type conditions but also a nice structure of the covariance operator.

引用

页码：1227 / 1263

页数：37

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