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On the parity of individuals in a branching process

Published online by Cambridge University Press:  14 July 2016

J. Gani  and
I. W. Saunders
J. Gani
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
I. W. Saunders
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
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Abstract

This paper is concerned with the parity of a population of yeast cells, each of which may bud, not bud or die. Two multitype models are considered: a Galton-Watson process in discrete time, and its analogous birth-death process in continuous time. The mean number of cells with parity 0, 1, 2, … is obtained in both cases; some simple results are also derived for the second moments of the two processes.

Keywords

YEAST CELLSPARITYMULTITYPE GALTON-WATSON PROCESSMULTITYPE BIRTH-DEATH PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 219 - 230
Copyright
Copyright © Applied Probability Trust 1976 

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References

Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
Pollard, J. H. (1975) Modelling human populations for projection purposes — some of the problems and challenges. Austral. J. Statist. 17, 63–76.CrossRefGoogle Scholar
Saunders, I. W. (1976) A convergence theorem for parities in a birth and death process. J. Appl. Prob. 13, 231–238.Google Scholar