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.
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页码：559 / 580
页数：22
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