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Yule process approximation for the skeleton of a branching process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Neil O'Connell
Neil O'Connell*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Statistics, University of California, Berkeley, CA 94720, USA.
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Abstract

The skeleton of a (super-) critical Galton-Watson process with offspring mean 1 + r, r ≧ 0, and finite offspring variance, is considered. When r = 0 it is trivial. If r > 0 is small and the time unit is taken as α /r generations (α > 0) then the skeleton can be approximated by a Yule (linear pure birth) process of rate α. This approximation can be used to study the evolution of genetic types over a long period of time in an exponentially growing population.

Keywords

DECOMPOSITION OF BRANCHING PROCESSESSUPERCRITICALPURE BIRTH PROCESSHARRIS–SEVAST'YANOV TRANSFORMATIONDIFFUSION APPROXIMATION

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 725 - 729
Copyright
Copyright © Applied Probability Trust 1993 

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References

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