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On a class of multivariate counting processes

Part of: Special processes Applications

Published online by Cambridge University Press:  10 June 2016

Ji Hwan Cha  and
Massimiliano Giorgio
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Massimiliano Giorgio*
Affiliation:
Second University of Naples
*
* Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: jhcha@ewha.ac.kr
** Postal address: Department of Industrial and Information Engineering, Second University of Naples, 81031, Aversa (CE), Italy. Email address: massimiliano.giorgio@unina2.it
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Abstract

In this paper we define and study a new class of multivariate counting processes, named `multivariate generalized Pólya process'. Initially, we define and study the bivariate generalized Pólya process and briefly discuss its reliability application. In order to derive the main properties of the process, we suggest some key properties and an important characterization of the process. Due to these properties and the characterization, the main properties of the bivariate generalized Pólya process are obtained efficiently. The marginal processes of the multivariate generalized Pólya process are shown to be the univariate generalized Pólya processes studied in Cha (2014). Given the history of a marginal process, the conditional property of the other process is also discussed. The bivariate generalized Pólya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Pólya process.

Keywords

Multivariate generalized Pólya processmarginal processcomplete stochastic intensity functiondependence structureconditional counting process

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62P30: Applications in engineering and industry
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 443 - 462
Copyright
Copyright © Applied Probability Trust 2016 

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