一类Gauss序列极值的极限律

Limit Laws for Extremes of a Class of Gaussian Sequences

中文关键词:  cox-过程  水平超过  最大值  非平稳  渐近分布.

英文关键词:cox-process  exceedance of levels  maxima  nonstationary  asymptotic distribution.

中文摘要:

      本文讨论一类非平稳Gauss序列的极值.利用点过程收敛定理得到多水平超过的点过程的收敛性,同时得到在不相交区间上最大值的联合渐近分布,第$k$个最大值的渐近分布以及前$r$个极值的联合渐近状态.

英文摘要:

      In this paper, we discuss the extremes of a class of nonstationary Gaussian sequences. We apply the convergence theorem of the point process theory to obtain the convergence of the point process of more level's exceedances. Moreover, the asymptotic distribution of the maxima in disjoint intervals is obtained. The asymptotic distribution of $k$-th largest maxima and the asymptotic joint distribution for a finite number of the $r$th largest maxima are also obtained.