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A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes

Published online by Cambridge University Press:  14 July 2016

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

In a class of population-size-dependent Galton-Watson processes where extinction does not occur with probability 1 we describe the rate of decay of qi (the probability that the process starting from i ancestors will become extinct) as the number i of ancestors increases.

The results are related to the asymptotic behavior of the Green's function of the critical Galton-Watson process with immigration.

Keywords

STATE DEPENDENCEIMMIGRATIONEXTINCTIONGREEN'S FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 920 - 925
Copyright
Copyright © Applied Probability Trust 1985 

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