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On some classes of population-size-dependent Galton–Watson processes

Published online by Cambridge University Press:  14 July 2016

Reinhard Höpfner
Reinhard Höpfner*
Affiliation:
Johannes-Gutenberg-Universität Mainz
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Abstract

Some classes of population-size-dependent Galton–Watson processes {Z(t)}t=0,1, …, whose transition probability generating functions allow for certain upper or lower bounds, can be treated by means of functional iteration methods. Criteria for almost certain extinction are obtained as well as gammatype limit distributions for Z(t)/t as t → ∞ the results can be stated under conditions on moments of the reproduction distributions.

Keywords

BRANCHING PROCESSIMMIGRATIONPROBABILITY OF EXTINCTIONLIMIT DISTRIBUTIONS

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Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985, pp. 25 - 36
Copyright
Copyright © Applied Probability Trust 1985 

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