Multitype branching processes with inhomogeneous Poisson immigration

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 uncondi...

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Bibliographic Details
Published in:Advances in applied probability 2018-12, Vol.50 (A), p.211-228
Main Authors: Mitov, Kosto V., Yanev, Nikolay M., Hyrien, Ollivier
Format: Article
Language:English
Subjects:
Asymptotic properties
Branching (mathematics)
Fractals
Immigration
Markov processes
Original Article
Poisson distribution
Probability
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2018.81