Almost sure limit theorems for the maximum of stationary Gaussian sequences

被引：78

作者：

Csáki, E

Gonchigdanzan, K

机构：

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Hungarian Acad Sci, Inst Math, H-1364 Budapest, Hungary

来源：

STATISTICS & PROBABILITY LETTERS | 2002年 / 58卷 / 02期

关键词：

almost sure central limit theorem; logarithmic average; stationary Gaussian sequence;

D O I：

10.1016/S0167-7152(02)00128-1

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 prove an almost sure limit theorem for the maxima of stationary Gaussian sequences with covariance r(n) under the condition r(n)logn(log log n)(1+epsilon) = O(1). (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：195 / 203

页数：9

共 8 条

[1] A universal result in almost sure central limit theory [J].

Berkes, I ;

Csáki, E .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2001, 94 (01) :105-134

[2] Results and problems related to the pointwise central limit theorem [J].

Berkes, I .

ASYMPTOTIC METHODS IN PROBABILITY AND STATISTICS: A VOLUME IN HONOUR OF MIKLOS CSORGO, 1998, :59-96

[3]

BERKES I, 2000, STOCHASTIC PROCESS A, V91, P77

[4] Almost sure convergence in extreme value theory [J].

Cheng, SH ;

Peng, L ;

Qi, YC .

MATHEMATISCHE NACHRICHTEN, 1998, 190 :43-50

[5] On almost sure max-limit theorems [J].

Fahrner, I ;

Stadtmuller, U .

STATISTICS & PROBABILITY LETTERS, 1998, 37 (03) :229-236

[6] A strong invariance principle for the logarithmic average of sample maxima [J].

Fahrner, I .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2001, 93 (02) :317-337

[7]

Leadbetter M. R., 1983, Springer Series in Statistics, DOI 10.1007/978-1-4612-5449-2

[8]

Weber M., 2000, EXPO MATH, V18, P97

← 1 →