A STRONG INVARIANCE-PRINCIPLE CONCERNING THE J-UPPER ORDER-STATISTICS FOR STATIONARY GAUSSIAN SEQUENCES
成果类型：
Article
署名作者：
HAIMAN, G; PURI, ML
署名单位：
Indiana University System; Indiana University Bloomington
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989395
发表日期：
1993
页码：
86-135
关键词：
摘要：
It is shown that in the case of stationary Gaussian processes, the Jth (J greater-than-or-equal-to 1) record times {T(n), n greater-than-or-equal-to 1} and the corresponding J-upper order statistics {X(Tn-J+1,Tn),...,X(Tn,Tn)} can almost surely be identified via a translation of the time index n to the corresponding elements defined on a sequence of independent and identically distributed random variables. A construction method for approximating sequences of record times and the corresponding upper order statistics introduced by Haiman (1987a, b) for the case J = 1 is extended and applied under weaker conditions concerning the covariance function, and also under different sets of new hypotheses.