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On the existence of the stable birth-type distribution in a general branching process cell cycle model with unequal cell division

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Marina Alexandersson
Marina Alexandersson*
Affiliation:
University of California, Berkeley
*
∗ Postal address: University of California, Department of Statistics, 367 Evans Hall #3860, Berkeley, CA 94720-3860, USA. Email address: marina@stat.berkeley.edu
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Abstract

We use multi-type branching process theory to construct a cell population model, general enough to include a large class of such models, and we use an abstract version of the Perron-Frobenius theorem to prove the existence of the stable birth-type distribution. The generality of the model implies that a stable birth-size distribution exists in most size-structured cell cycle models. By adding the assumption of a critical size that each cell has to pass before division, called the nonoverlapping case, we get an explicit analytical expression for the stable birth-type distribution.

Keywords

Branching processcell populationunequal cell divisionPerron-FrobeniusCrump-Mode-Jagersstable type distribution

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 92D25: Population dynamics (general)
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 685 - 695
Copyright
Copyright © by the Applied Probability Trust 2001 

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Footnotes

This work is part of the Bank of Sweden TercentenaryF oundation project ‘Dependence and Interaction in Stochastic Population Dynamics’.

References

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