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A fixed-point property for Galton–Watson processes with generation dependence

Published online by Cambridge University Press:  14 July 2016

Dean H. Fearn
Dean H. Fearn*
Affiliation:
California State University
*
∗Postal address: Department of Statistics, California State University, Hayward, CA 94542, U.S.A.
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Abstract

Conditions for the non-sure extinction of Galton-Watson processes with generation dependence are obtained. Also a condition is given for such processes to have a strictly increasing probability generating function.

Keywords

BRANCHING PROCESSESEXTINCTION PROBABILITYVARYING ENVIRONMENTGENERATION DEPENDENCEFIXED POINT FOR A FAMILY OF PROBABILITY GENERATING FUNCTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 514 - 519
Copyright
Copyright © Applied Probability Trust 

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References

[1] Church, J. D. (1971) On infinite composition of probability generating functions. Z. Wahrscheinlichkeitsth. 19, 243–256.Google Scholar
[2] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
[3] Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
[4] Jirina, M. (1976) Extinction of non-homogeneous Galton-Watson processes. J. Appl. Prob. 13, 132–137.Google Scholar