A new class of multivariate counting processes and its characterization
A new class of multivariate counting processes and its characterization
复制标题
一类新的多元计数过程及其表征
DOI：
10.1080/17442508.2018.1540625
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发表时间：
2018
期刊：
影响因子：
0.9
通讯作者：
M. Giorgio
中科院分区：
文献类型：
--
作者：
J. Cha;M. Giorgio
本文提出了一类新的多元计数过程，推广和推广了Cha和Giorgio最近研究的多元广义Polya过程[关于一类多元计数过程，Adv.Appl.可能吧。48(2016)，第443-462页]。首先，我们用混合的方法定义了这个多元计数过程。为了进一步描述这一过程，我们提出了另一种定义，这有助于对拟议过程的描述。我们还讨论了所提出的多元计数过程的相依结构和其他随机性质，如任意区间或不相交区间内事件数目的联合分布，以及给定事件数目时不同类型事件到达时间的条件联合分布。并刻画了相应的边际过程。
ABSTRACT In this paper, we suggest a new class of multivariate counting processes which generalizes and extends the multivariate generalized Polya process recently studied in Cha and Giorgio [On a class of multivariate counting processes, Adv. Appl. Probab. 48 (2016), pp. 443–462]. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We also discuss the dependence structure of the proposed multivariate counting process and other stochastic properties such as the joint distributions of the number of events in an arbitrary interval or disjoint intervals and the conditional joint distribution of the arrival times of different types of events given the number of events. The corresponding marginal processes are also characterized.