On Almost Sure Max-limit Theorems of Complete and Incomplete Samples from Stationary Sequences  

作　　者：Bin TONG Zuo Xiang PENG 

机构地区：[1]Financial Engineering Research Center, Shanghai Jiao Tong University, Shanghai 200052, P. R. China [2]School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第7期1323-1332,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 70371061） and the Program for Excellent Talents in Chongqing Higher Education Institutions （Grant No. 120060-20600204）Acknowledgements The authors would like to express their deep thanks to the referees for carefully reading the paper and for their comments which greatly improve the paper.

摘　　要：Let Mn denote the partial maximum of a strictly stationary sequence （Xn）. Suppose some of the random variables of （Xn） can be observed and let Mn stand for the maximum of observed random variables from the set {X1,..., Xn}. In this paper, the almost sure limit theorems related to random vector （Mn, Mn） are considered in terms of i.i.d, case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.Let Mn denote the partial maximum of a strictly stationary sequence （Xn）. Suppose some of the random variables of （Xn） can be observed and let Mn stand for the maximum of observed random variables from the set {X1,..., Xn}. In this paper, the almost sure limit theorems related to random vector （Mn, Mn） are considered in terms of i.i.d, case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.

关 键 词：Almost sure limit theorem MAXIMUM missing observations stationary Caussian sequence 

分 类 号：O211.4[理学—概率论与数理统计] O211.61[理学—数学]