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首页> 外文期刊>Annals of the Institute of Statistical Mathematics >Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays
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Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays

机译：稳态二元高斯三角阵列的簇和偏和点过程的联合行为

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摘要

For Gaussian stationary triangular arrays, it is well known that the extreme values may occur in clusters. Here we consider the joint behaviors of the point processes of clusters and the partial sums of bivariate stationary Gaussian triangular arrays. For a bivariate stationary Gaussian triangular array, we derive the asymptotic joint behavior of the point processes of clusters and prove that the point processes and partial sums are asymptotically independent. As an immediate consequence of the results, one may obtain the asymptotic joint distributions of the extremes and partial sums. We illustrate the theoretical findings with a numeric example.
机译：对于高斯稳态三角形阵列，众所周知，极值可能以簇的形式出现。在这里，我们考虑了簇的点过程的联合行为和二元稳态高斯三角阵列的部分和。对于一个双变量稳态高斯三角阵列，我们推导了簇点过程的渐近联合行为，并证明了点过程和偏和是渐近独立的。作为结果的直接结果，人们可以获得极值和部分和的渐近联合分布。我们用一个数字例子来说明理论结果。

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