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The rates of growth of the Galton-Watson process in varying environment

Published online by Cambridge University Press:  14 July 2016

James H. Foster  and
Robert T. Goettge
James H. Foster*
Affiliation:
University of Denver
Robert T. Goettge*
Affiliation:
University of Colorado
*
*Now at Weber State College, Ogden, Utah.
**Now with The Aerospace Corporation.
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Abstract

It is shown that a Galton-Watson process in varying environment, unlike a classical Galton-Watson process, can have an infinite (though at most countable) number of distinct rates of growth.

Keywords

GALTON–WATSON BRANCHING PROCESSVARYING ENVIRONMENTSRATES OF GROWTH
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 144 - 147
Copyright
Copyright © Applied Probability Trust 1976 

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References

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[4] Goettge, R. (1974) Limit theorems for the supercritical Galton-Watson process in varying environments. Math. Biosci., To appear.Google Scholar
[5] Jagers, P. (1974) Galton-Watson processes in varying environments. J. Appl. Prob. 11, 174–178.CrossRefGoogle Scholar
[6] Lindvall, T. (1974) Almost sure convergence of branching processes in varying and random environments. Ann. Prob. 2, 344–346.Google Scholar