Most of the multivariate counting processes studied in the literature are regular processes, which implies, ignoring the types of the events, the non-occurrence of multiple events. However, in practice, several different types of events may occur simultaneously. In this paper, a new class of multivariate counting processes which allow simultaneous occurrences of multiple types of events is suggested and its stochastic properties are studied. For the modeling of such kind of process, we rely on the tool of superposition of seed counting processes. It will be shown that the stochastic properties of the proposed class of multivariate counting processes are explicitly expressed. Furthermore, the marginal processes are also explicitly obtained. We analyze the multivariate dependence structure of the proposed class of counting processes.

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关于没有正则性的多变量广义聚亚过程

文献中研究的大多数多元计数过程是常规过程，这意味着，忽略事件的类型，多个事件的不发生。然而，在实践中，可能同时发生几种不同类型的事件。在本文中，提出了一类新的多元计数过程，它允许同时发生多种类型的事件，并研究了它的随机特性。对于此类过程的建模，我们依靠种子计数过程的叠加工具。将表明，所提出的多变量计数过程类的随机特性被明确表达。此外，还明确获得了边际过程。我们分析了所提出的计数过程类的多元依赖结构。