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Multitype branching processes with inhomogeneous Poisson immigration

Published online by Cambridge University Press:  01 February 2019

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
Corresponding
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Abstract

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.

Type
Original Article
Copyright
Copyright © Applied Probability Trust 2018 

References

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