Multitype branching process with non-homogeneous Poisson and contagious Poisson immigration

In a multitype branching process, it is assumed that immigrants arrive according to a non-homogeneous Poisson or a contagious Poisson process (both processes are formulated as a non-homogeneous birth process with an appropriate choice of transition intensities). We show that the normalized numbers o...

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Bibliographic Details
Published inJournal of applied probability Vol. 58; no. 4; pp. 1007 - 1042
Main Authors Rabehasaina, Landy, Woo, Jae-Kyung
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2021
Applied Probability Trust
Subjects
Behavior
Epidemics
Epidemiology
Immigration
Original Article
Poisson density functions
Reinsurance
Research Papers
Theorems
contagious Poisson process
non-homogeneous Poisson process
60J85
convergence in distribution
90B15
60J80
Multitype branching process with immigration
60K25
60K10
Online AccessGet full text
ISSN0021-9002
1475-6072
DOI10.1017/jpr.2021.19

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Summary:In a multitype branching process, it is assumed that immigrants arrive according to a non-homogeneous Poisson or a contagious Poisson process (both processes are formulated as a non-homogeneous birth process with an appropriate choice of transition intensities). We show that the normalized numbers of objects of the various types alive at time t for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, we provide some transient expectation results when there are only two types of particles.
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ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2021.19