An almost sure limit theorem for the maxima of smooth stationary Gaussian processes

被引：9

作者：

Tan, Zhongquan ^{[1
]}

机构：

[1] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2013年 / 83卷 / 09期

基金：

美国国家科学基金会;

关键词：

Almost sure limit theorem; Maximum; Stationary Gaussian process; Smooth Gaussian process; CONVERGENCE; EXTREMES; ASYMPTOTICS; SEQUENCES; SUPREMUM; TIME;

D O I：

10.1016/j.spl.2013.05.034

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：

Let {X(t), t >= 0} be a continuous mean square differentiable stationary Gaussian process. Under some mild restrictions on its correlation function r(.), we prove an almost sure limit theorem for the maximum of the Gaussian process {X(t), t >= 0}. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：2135 / 2141

页数：7

共 50 条

[1] AN ALMOST SURE LIMIT THEOREM FOR THE MAXIMA OF MULTIVARIATE STATIONARY GAUSSIAN SEQUENCES
Chen, Zhicheng
Peng, Zuoxiang
Zhang, Hongyun
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 86 (03) : 315 - 321
[2] Almost sure central limit theorem for the maxima and sums of stationary Gaussian sequences
Zhongquan Tan
Yuebao Wang
[J]. Journal of the Korean Statistical Society, 2011, 40 : 347 - 355
[3] Almost sure central limit theorem for the maxima and sums of stationary Gaussian sequences
Tan, Zhongquan
Wang, Yuebao
[J]. JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2011, 40 (03) : 347 - 355
[4] ALMOST SURE LIMIT POINTS OF MAXIMA OF STATIONARY GAUSSIAN SEQUENCES
HEBBAR, HV
[J]. ANNALS OF PROBABILITY, 1980, 8 (02): : 393 - 399
[5] Almost sure limit theorem for stationary Gaussian random fields
Choi, Hyemi
[J]. JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2010, 39 (04) : 449 - 454
[6] ALMOST SURE LIMIT THEOREM FOR THE MAXIMA OF STRONGLY DEPENDENT GAUSSIAN SEQUENCES
Lin, Fuming
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2009, 14 : 224 - 231
[7] Almost sure limit theorem for stationary Gaussian random fields
Hyemi Choi
[J]. Journal of the Korean Statistical Society, 2010, 39 : 449 - 454
[8] Almost Sure Central Limit Theorem for strictly stationary processes
Lesigne, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (06) : 1751 - 1759
[9] Almost Sure Limit Theorem for the Order Statistics of Stationary Gaussian Sequences
Chen, Yang
Tan, Zhongquan
[J]. FILOMAT, 2018, 32 (09) : 3355 - 3364
[10] The improved results in almost sure central limit theorem for the maxima of strongly dependent stationary Gaussian vector sequences
Xiang Zeng
Qunying Wu
[J]. Journal of Inequalities and Applications, 2015

← 1 2 3 4 5 →