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Multitype branching processes with inhomogeneous Poisson immigration

Part of: Limit theorems Markov processes Applications

Published online by Cambridge University Press:  01 February 2019

Kosto V. Mitov ,
Nikolay M. Yanev  and
Ollivier Hyrien
Kosto V. Mitov*
Affiliation:
Vasil Levski National Military University
Nikolay M. Yanev*
Affiliation:
Bulgarian Academy of Sciences
Ollivier Hyrien*
Affiliation:
Fred Hutchinson Cancer Research Center
*
Faculty of Aviation, Vasil Levski National Military University, 5856 D. Mitropolia, Pleven, Bulgaria. Email address: kmitov@yahoo.com
Department of Operations Research, Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria. Email address: yanev@math.bas.bg
Program in Biostatistics, Bioinformatics, and Epidemiology, Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA. Email address: ohyrien@fredhutch.org
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Abstract

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In this paper we introduce multitype branching processes with inhomogeneous Poisson immigration, and consider in detail the critical Markov case when the local intensity r(t) of the Poisson random measure is a regularly varying function. Various multitype limit distributions (conditional and unconditional) are obtained depending on the rate at which r(t) changes with time. The asymptotic behaviour of the first and second moments, and the probability of nonextinction are investigated.

Keywords

Multitype branching processimmigrationinhomogeneous Poisson processlimit distribution

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F05: Central limit and other weak theorems 60J85: Applications of branching processes 62P10: Applications to biology and medical sciences
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 211 - 228
Copyright
Copyright © Applied Probability Trust 2018 

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