The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences

被引：15
|
作者：
Ski, Marcin Dudzi [1 ]
机构：
[1] Agr Univ Warsaw, Dept Econometr & Stat, PL-02787 Warsaw, Poland
来源：
STATISTICS & PROBABILITY LETTERS | 2008年 / 78卷 / 04期
关键词：
almost sure central limit theorem; extreme values; partial sums; stationary Gaussian sequences; associated random variables; slowly varying functions at infinity; Karamata's theorem;
D O I：
10.1016/j.spl.2007.07.007
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：
Suppose that X1,X2,... is a standardized stationary Gaussian sequence. Let: M-n:=max(X-1,...,X-n), S-n:=Sigma(n)(i=1) X-i, sigma(n):=root Var(S-n), and a(n) > 0, b(n) denote suitable normalizing constants. Our goal is to prove the almost sure central limit theorem for the sequence {a(n)(M-n - b(n)), S-n/sigma(n)), under certain additional assumptions on the covariance function r(t):= Cov(X-1, X1+t). (c) 2007 Elsevier B.V. All rights reserved.
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页码：347 / 357
页数：11
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