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Applications of the age distribution in age dependent branching processes

Published online by Cambridge University Press:  14 July 2016

Howard J. Weiner
Howard J. Weiner*
Affiliation:
University of California, Davis
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Extract

This paper considers asymptotic properties of increasing population age dependent branching processes which have a limiting age distribution. In Section I, the Bellman-Harris model [2] is altered in accord with a suggestion by Kendall [3]. The effect of this modification on the applicable results of [3] is indicated. An extension to the case where each cell passes through a sequence of states to mitosis or proceeds from state to state in accord with a semi-Markov process to mitosis is considered. Section 1.1 considers asymptotic moments for the total number of cells. Section 1.2 treats moments in a sequence-of-states model [4]. Section 1.3 extends the results of 1.2 to a semi-Markov model. Section 1.4 treats various asymptotic lifetime distributions and fraction of cells in a given state for both the sequence-of-states and semi-Markov models.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 1 , June 1966 , pp. 179 - 201
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Cox, D. R. (1962) Renewal Theory, Methuen, London.Google Scholar
[2] Harris, T. E. (1963) The Theory of Branching Processes, Prentice-Hall and Springer, Berlin.Google Scholar
[3] Kendall, D. G. (1952) On the choice of a mathematical model to represent normal bacterial content. J. Roy. Statist. Soc. Ser. B. 14 No. 1, 41–44.Google Scholar
[4] Weiner, H. J. (1964) On age dependent branching processes. Stanford University Technical Report No. 94 Nonr 225(52) (NR 342–022).Google Scholar