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.
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.
