A NEW PROOF OF AN OLD RESULT BY PICKANDS

被引：21
作者：
Albin, J. M. P. [1 ]
Choi, H. [2 ,3 ]
机构：
[1] Chalmers, Dept Math, S-41296 Gothenburg, Sweden
[2] Chonbuk Natl Univ, Dept Stat, Jeonju 561756, South Korea
[3] Chonbuk Natl Univ, Inst Appl Stat, Jeonju 561756, South Korea
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2010年 / 15卷
基金：
新加坡国家研究基金会;
关键词：
Stationary Gaussian process; Pickands constant; extremes; ASYMPTOTIC PROPERTIES; STATIONARY-PROCESSES; GAUSSIAN PROCESS; TAILS;
D O I：
10.1214/ECP.v15-1566
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 {xi(t)}(t is an element of[0,h]) be a stationary Gaussian process with covariance function r such that r(t) = 1 - C vertical bar t vertical bar(alpha) + o(vertical bar t vertical bar(alpha)) as t -> 0. We give a new and direct proof of a result originally obtained by Pickands, on the asymptotic behaviour as u -> infinity of the probability P{sup(t is an element of vertical bar 0,h vertical bar) xi(t) > u} that the process xi exceeds the level u. As a by-product, we obtain a new expression for Pickands constant H alpha
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页码：339 / 345
页数：7
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