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Multitype branching processes with inhomogeneous Poisson immigration

  • Kosto V. Mitov (a1), Nikolay M. Yanev (a2) and Ollivier Hyrien (a3)

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.

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Copyright

Corresponding author

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

References

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Keywords

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Multitype branching processes with inhomogeneous Poisson immigration

  • Kosto V. Mitov (a1), Nikolay M. Yanev (a2) and Ollivier Hyrien (a3)

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