连续与离散时间Gauss次序统计过程的极值  

On the maxima of continuous and discrete time Gaussian order statistics processes

作　　者：谭中权[1] Zhongquan Tan

机构地区：[1]嘉兴学院数理与信息工程学院,嘉兴314001

出　　处：《中国科学：数学》2018年第5期623-642,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11501250和61703183);浙江省自然科学基金(批准号:LY18A010020);中国博士后科学基金(批准号:2016M600460)资助项目

摘　　要：本文研究一类由平稳Gauss过程生成的Gauss次序统计过程的极值与该过程离散化后的极值的渐近关系.结果表明,当Gauss过程是弱相依并且离散化格点足够稀疏时,这两个极值之间是渐近独立的,否则这两个极值之间是渐近相依的.In this paper, we study the asymptotic relation between the maximum of a continuous order statistics process formed by stationary Gaussian processes and the maximum of this process sampled at discrete time points. It is shown that, these two maxima are asymptotically independent when the Gaussian processes are weakly dependent and the discrete points are sufficiently sparse, while for other cases, these two maxima are asymptotically dependent.

关 键 词：GAUSS过程 连续时间过程 离散时间过程 极值 次序统计过程 

分 类 号：O211[理学—概率论与数理统计]