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ON A MULTIVARIATE GENERALIZED POLYA PROCESS WITHOUT REGULARITY PROPERTY

Published online by Cambridge University Press:  24 April 2019

Ji Hwan Cha  and
F.G. Badía
Ji Hwan Cha
Affiliation:
Department of Statistics, Ewha Womans University, Seoul120-750, Republic of Korea E-mail: jhcha@ewha.ac.kr
F.G. Badía
Affiliation:
Department of Statistical Methods, University of Zaragoza, Zaragoza50018, Spain E-mail: gbadia@unizar.es
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Abstract

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.

Keywords

characterization of multivariate counting processescomplete intensity functionsdependence structuregeneralized polya processsuperposition
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 4 , October 2020 , pp. 484 - 506
Copyright
Copyright © Cambridge University Press 2019

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