高斯三角阵的聚集点过程与部分和的联合渐近行为

Abstract

Abstract:

Let $\{X_{i,n},1\leq i\leq n\}$ be a centered stationary Gaussian triangular array with unit variance. Assuming the correlation $ \rho_{j,n}=E\left( X_{i,n}X_{i+j,n}\right)$ satisfies the conditions in [14], this paper is interested in the joint behavior of the point process of clusters and the partial sum of the Gaussian triangular array. It is shown that the point process of clusters converges in distribution to a Poisson process and is asymptotically independent with the partial sums.

Key words: Stationary gaussian triangular array, Point process of clusters, Partial sum, Joint behavior

CLC Number:

O211.4

Lu Yingyin, Zhang Wenjing, Guo Jinhui. Joint Behavior of Point Process of Clusters and Partial Sum for a Gaussian Triangular Array[J].Acta mathematica scientia,Series A, 2024, 44(5): 1311-1318.

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Joint Behavior of Point Process of Clusters and Partial Sum for a Gaussian Triangular Array

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