On a class of multivariate counting processes
On a class of multivariate counting processes
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关于一类多元计数过程
DOI：
10.1017/apr.2016.9
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发表时间：
2016
影响因子：
1.2
通讯作者：
M. Giorgio
中科院分区：
文献类型：
--
作者：
J. Cha;M. Giorgio
摘要本文定义并研究了一类新的多元计数过程，称为“多元广义Pólya过程”。首先对二元广义Pólya过程进行了定义和研究，并简要讨论了其可靠性应用。为了推导出该工艺的主要性质，我们提出了该工艺的一些关键性质和一个重要特征。由于这些性质和表征，有效地得到了二元广义Pólya过程的主要性质。多元广义Pólya过程的边际过程为Cha（2014）研究的单变量广义Pólya过程。给定一个边缘过程的历史，也讨论了另一个过程的条件性质。将二元广义Pólya过程推广到多元情形。定义了多变量点过程的依赖关系概念，并在此基础上分析了多变量广义Pólya过程的依赖关系结构。
Abstract In this paper we define and study a new class of multivariate counting processes, named `multivariate generalized Pólya process'. Initially, we define and study the bivariate generalized Pólya process and briefly discuss its reliability application. In order to derive the main properties of the process, we suggest some key properties and an important characterization of the process. Due to these properties and the characterization, the main properties of the bivariate generalized Pólya process are obtained efficiently. The marginal processes of the multivariate generalized Pólya process are shown to be the univariate generalized Pólya processes studied in Cha (2014). Given the history of a marginal process, the conditional property of the other process is also discussed. The bivariate generalized Pólya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Pólya process.