Extremes of Gaussian processes, on results of Piterbarg and Seleznjev

被引：12
|
作者：
Hüsler, J [1 ]
机构：
[1] Univ Bern, Inst Stat Math, CH-3012 Bern, Switzerland
来源：
STATISTICS & PROBABILITY LETTERS | 1999年 / 44卷 / 03期
关键词：
Gaussian processes; maxima; extreme values; exceedances; Poisson point process; Berman's condition;
D O I：
10.1016/S0167-7152(99)00016-4
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：
For a particular sequence of Gaussian processes we consider the maximum M-n(T) up to time T and its limiting behaviour as T = T(n) and n converges to oo. This sequence occurs in the approximation of the path of the continuous Gaussian process by broken lines. This limiting behaviour was analyzed by Piterbarg and Seleznjev assuming certain conditions. We improve their result assuming a weaker long-range dependence condition. (C) 1999 Elsevier Science B.V. All rights reserved.
引用
下载
收藏
页码：251 / 258
页数：8
相关论文
共 50 条
  • [21] On asymptotic constants in the theory of extremes for Gaussian processes
    Dieker, A. B.
    Yakir, B.
    BERNOULLI, 2014, 20 (03) : 1600 - 1619
  • [22] Extremes of threshold-dependent Gaussian processes
    Bai, Long
    Debicki, Krzysztof
    Hashorva, Enkelejd
    Ji, Lanpeng
    SCIENCE CHINA-MATHEMATICS, 2018, 61 (11) : 1971 - 2002
  • [23] EXTREMES OF GAUSSIAN-PROCESSES WITH BIMODAL SPECTRA
    TORO, GR
    CORNELL, CA
    JOURNAL OF ENGINEERING MECHANICS-ASCE, 1986, 112 (05): : 465 - 484
  • [24] Extremes of Gaussian Processes with a Smooth Random Trend
    Piterbarg, Vladimir
    Popivoda, Goran
    Stamatovic, Sinisa
    FILOMAT, 2017, 31 (08) : 2267 - 2279
  • [25] Extremes of threshold-dependent Gaussian processes
    Long Bai
    Krzysztof Debicki
    Enkelejd Hashorva
    Lanpeng Ji
    Science China Mathematics, 2018, 61 (11) : 1971 - 2002
  • [26] Extremes of space-time Gaussian processes
    Kabluchko, Zakhar
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (11) : 3962 - 3980
  • [27] Extremes of vector-valued Gaussian processes
    Debicki, Krzysztof
    Hashorva, Enkelejd
    Wang, Longmin
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (09) : 5802 - 5837
  • [28] Extremes of threshold-dependent Gaussian processes
    Long Bai
    Krzysztof Dȩbicki
    Enkelejd Hashorva
    Lanpeng Ji
    Science China Mathematics, 2018, 61 : 1971 - 2002
  • [29] On Piterbarg theorem for maxima of stationary Gaussian sequences
    Enkelejd Hashorva¹
    Zuoxiang Peng²
    Zhichao Weng³
    Lithuanian Mathematical Journal, 2013, 53 : 280 - 292
  • [30] Extremes of Gaussian and non-Gaussian vector processes: a geometric approach
    Leira, BJ
    STRUCTURAL SAFETY, 2003, 25 (04) : 401 - 422
12345