具有随机足标的高斯序列的部分和与最大值的渐近联合分布

The Asymptotic Joint Distribution of Maximum and Sum of Gaussian Sequence with Random Sample Size

设 {Xi,i≥ 1}是标准高斯序列 ,具有EXi =0 ,EX2 i =1,rij =cov(XI,Xj)。本文得到了rij 满足一定条件时 ,具有随机足标的最大值与部分和的联合渐近分布 ,平稳情形则作为特例被给出。

Let｛X i,i≥1｝ be a standard Gaussian sequence of random variables with EX i=0,EX 2 i=1,r ij =cov(X i,X j).The asymptotic joint distribution of maximum and sum of Gaussian sequence with random sample size are obtained under some conditions that depended on r ij , The case of stationary sequence is give as an example.