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.

中文翻译：

---

固定二元高斯三角阵列簇点过程与部分和的联合行为

对于高斯平稳三角形阵列，众所周知，极值可能出现在簇中。在这里，我们考虑簇的点过程的联合行为和二元平稳高斯三角阵列的部分和。对于一个二元平稳高斯三角阵列，我们推导了簇点过程的渐近联合行为，证明了点过程和部分和是渐近独立的。作为结果的直接结果，可以得到极值和部分和的渐近联合分布。我们用一个数值例子来说明理论发现。