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Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

Published online by Cambridge University Press:  22 June 2017

Ollivier Hyrien
Affiliation:
Fred Hutchinson Cancer Research Center
Kosto V. Mitov
Affiliation:
Vasil Levski National Military University
Nikolay M. Yanev
Affiliation:
Bulgarian Academy of Sciences
Corresponding

Abstract

We consider a class of Sevastyanov branching processes with nonhomogeneous Poisson immigration. These processes relax the assumption required by the Bellman–Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include a novel law of large numbers and a central limit theorem which emerge from the nonhomogeneity of the immigration process.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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References

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