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Convergence of critical Galton-Watson branching processes

Published online by Cambridge University Press:  14 July 2016

Torgny Lindvall
Torgny Lindvall*
Affiliation:
University of Göteborg, Sweden
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Abstract

The purpose of this note is to extend results on critical Galton-Watson branching processes, due to Feller and Lamperti: if the number of individuals at time zero tends to infinity, the process converges, with two different normalizations, to certain diffusion processes in the functional form, discussed in, e.g., Billingsley.

Keywords

CONVERGECRITICAL BRANCHING PROCESSDIFFUSION PROCESSFUNCTIONAL FORMEXTENDING LAMPERTI
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 445 - 450
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley & Sons, New York.Google Scholar
[2] Lamperti, J. (1967) Limiting distibutions for branching processes. Proc. Fifth Berkeley Symp. Math. Statist. and Prob. 225–241. University of California Press.Google Scholar
[3] Lamperti, J. (1967) The limit of a sequence of branching processes. Z. Wahrscheinlichkeitsth. 7, 271–288.CrossRefGoogle Scholar
[4] Gikhman, I. I. and Skorohod, A. V. (1969) Introduction to the Theory of Random Processes. W.B. Sanders Company, London. (English translation).Google Scholar
[5] Harris, T. (1963) The Theory of Branching Processes. Springer, Berlin.Google Scholar