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Conditions for extinction in certain bisexual Galton–Watson branching processes

Published online by Cambridge University Press:  14 July 2016

David M. Hull
David M. Hull*
Affiliation:
Valparaiso University
*
∗ Postal address: Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, IN 46383, U.S.A.
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Abstract

A multitype branching process, the n-family community mating process, is introduced for the purpose of comparing extinction probabilities with those of bisexual Galton–Watson branching processes. Consideration of known properties of standard multitype branching processes leads to conditions which are both necessary and sufficient for extinction in a bisexual Galton–Watson branching process. An application is then made to the counterexample of the author's earlier paper.

Keywords

N-FAMILY COMMUNITY MATING PROCESSSUPERADDITIVE TWO-PLACE FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 414 - 418
Copyright
Copyright © Applied Probability Trust 1984 

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References

Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Hull, D. M. (1982) A necessary condition for extinction in those bisexual Galton–Watson branching processes governed by superadditive mating functions. J. Appl. Prob. 19, 847–850.CrossRefGoogle Scholar
Marshall, A. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar