Pair correlations and U-statistics for independent and weakly dependent random variables

被引：8

作者：

Berkes, I

Philipp, W

Tichy, R

机构：

[1] Hungarian Acad Sci, Inst Math, H-1053 Budapest, Hungary

[2] Univ Illinois, Dept Stat, Urbana, IL 61801 USA

[3] Graz Tech Univ, Inst Math A, A-8010 Graz, Austria

来源：

ILLINOIS JOURNAL OF MATHEMATICS | 2001年 / 45卷 / 02期

关键词：

D O I：

10.1215/ijm/1258138356

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a Glivenko-Cantelli type strong law of large numbers for the pair correlation of independent random variables. Except for a few powers of logarithms the results obtained are sharp. Similar estimates hold for the pair correlation of lacunary sequences {n(k)omega} mod 1.

引用

页码：559 / 580

页数：22

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