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A note on the Harris-Sevast'yanov transformation for supercritical branching processes

Part of: Markov processes

Published online by Cambridge University Press:  09 April 2009

H.-J. Schuh
H.-J. Schuh
Affiliation:
Department of Statistics, University of Melbourne, Melbourne, Victoria, Australia
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Abstract

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We show that the Harris-Sevast'yanov transformation for supercritical Galton-Watson processes with positive extinction probability q can be modified in such a way that the extinction probability of the new process takes any value between 0 and q. We give a probabilistic interpretation for the new process. This note is closely related to Athreya and Ney (1972), Chapter 1.12.

Keywords

supercritical Galton-Watson processextinction probabilityprobability generating functionHarris-Sevast'yanov transformation.

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 2 , April 1982 , pp. 215 - 222
Copyright
Copyright © Australian Mathematical Society 1982

References

Athreya, K. B. and Karlin, S. (1967), ‘Limit theorems for the split times of branching processes’, J. Math. Mech. 17, 257–277.Google Scholar
Athreya, K. B. and Ney, P. E. (1972), Branching Processes (Springer-Verlag, Berlin).CrossRefGoogle Scholar
Harris, T. E. (1948), ‘Branching processes’, Ann. Math. Statist. 19, 474–494.CrossRefGoogle Scholar
Harris, T. E. (1963), The Theory of Branching Processes (Springer-Verlag, Berlin).CrossRefGoogle Scholar