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Bounds for Certain Branching Processes

Published online by Cambridge University Press:  14 July 2016

Edward Pollak
Edward Pollak*
Affiliation:
Iowa State University, Ames, Iowa
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Summary

We consider a branching process for which the offspring distribution has the generating function f(t) and mean f'(1) = m < 1. The probability that a line descended from an individual still survives in generation n is asymptotically of the form cmn. A method is derived whereby good bounds for c may be obtained. This method makes use of the first three moments of the distribution of offspring.

Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 201 - 204
Copyright
Copyright © Applied Probability Trust 

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References

[1] Harris, T. E. (1963) The Theory of Branching Processes. Springer Verlag, Berlin, Gottingen, Heidelberg.Google Scholar
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[3] Kolmogorov, A. N. (1938) Zur Lösung einer biologischen Aufgabe. Comm. Math. Mech. Chebychev Univ., Tomsk. 2, 1–6.Google Scholar
[4] Seneta, E. (1967) On the transient behaviour of a Poisson branching process. J. Aust. Math. Soc. 7, 465–480.Google Scholar