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Some results on population-size-dependent Galton-Watson processes

Published online by Cambridge University Press:  14 July 2016

Reinhard Höpfner
Reinhard Höpfner*
Affiliation:
Albert-Ludwigs-Universität, Freiburg
*
∗Postal address: Institut für Mathematische Stochastik, Albert-Ludwigs-Universität, Hebelstr. 27, D-7800 Freiburg, W. Germany.
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Abstract

Some classes of population-size-dependent Galton-Watson processes are considered where extinction occurs with probability 1. Results on the asymptotic behaviour of the probability of survival up to time t, mean population size and conditioned limit distributions are found to hold. They correspond to those obtained in the study of Galton-Watson processes with immigration stopped at 0.

Keywords

STATE DEPENDENCEIMMIGRATIONEXTINCTION-TIME DISTRIBUTIONLIMIT DISTRIBUTIONS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 297 - 306
Copyright
Copyright © Applied Probability Trust 1986 

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