The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index

被引：0
|
作者：
Zhong Quan TAN [1 ]
机构：
[1] College of Mathematics, Physics and Information Engineering, Jiaxing University
来源：
Acta Mathematica Sinica,English Series | 2014年 / 30卷 / 06期
基金：
美国国家科学基金会;
关键词：
Limit theorem; weak convergence; maximum; random index; stationary Gaussian process;
D O I：
暂无
中图分类号：
O211.6 [随机过程];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let {X(t), t ≥ 0} be a standard(zero-mean, unit-variance) stationary Gaussian process with correlation function r(·) and continuous sample paths. In this paper, we consider the maxima M(T) = max{X(t), t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M(TT) exists under some additional conditions related to the correlation function r(·).
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页码：1021 / 1032
页数：12
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