A new class of marginally regular multivariate counting processes generated by the mixture of multivariate Poisson processes

Ji Hwan Cha, F. G. Badía

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, a new class of marginally regular multivariate counting processes is developed and its stochastic properties are studied. The dependence of the proposed multivariate counting process is generated from two sources: by means of mixing and by sharing a common counting process. Even under a rather complex dependence structure, the stochastic properties of the multivariate process and its marginal processes are mathematically tractable. 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 derive the properties of the proposed multivariate counting process and analyze the multivariate dependence structure of the class.

Original languageEnglish
JournalCommunications in Statistics - Theory and Methods
DOIs
StateAccepted/In press - 2020

Keywords

  • complete intensity functions
  • dependence structure
  • Generalized Polya process
  • marginally regular multivariate counting process

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