The limit theorems for maxima of stationary Gaussian processes with random Index

被引：0
|
作者：
Zhong Quan Tan
机构：
[1] Jiaxing University,College of Mathematics, Physics and Information Engineering
来源：
Acta Mathematica Sinica, English Series | 2014年 / 30卷
关键词：
Limit theorem; weak convergence; maximum; random index; stationary Gaussian process; 60G70; 60G15;
D O I：
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学科分类号：
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：11
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