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

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  • Ji Hwan Cha
  • F. G. Badía

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.

Suggested Citation

  • Ji Hwan Cha & F. G. Badía, 2022. "A new class of marginally regular multivariate counting processes generated by the mixture of multivariate Poisson processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(13), pages 4235-4251, June.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:13:p:4235-4251
    DOI: 10.1080/03610926.2020.1812652
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