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

作　　者：Zhong Quan TAN 

机构地区：[1]College of Mathematics, Physics and Information Engineering, Jiaxing University

出　　处：《Acta Mathematica Sinica,English Series》2014年第6期1021-1032,共12页数学学报（英文版）

基　　金：Supported by National Science Foundation of China(Grant No.11326175);Research Start-up Foundation of Jiaxing University(Grant No.70512021)

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（·）.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（·）.

关 键 词：Limit theorem weak convergence MAXIMUM random index stationary Gaussian process 

分 类 号：O211.6[理学—概率论与数理统计]