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Branching processes with varying and random geometric offspring distributions

Published online by Cambridge University Press:  14 July 2016

Niels Keiding  and
John E. Nielsen
Niels Keiding
Affiliation:
University of Copenhagen
John E. Nielsen
Affiliation:
University of Copenhagen
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Abstract

The class of fractional linear generating functions is used to illustrate various aspects of the theory of branching processes in varying and random environments. In particular, it is shown that Church's theorem on convergence of the varying environments process admits of an elementary proof in this particular case. For random environments, examples are given on the asymptotic behavior of extinction probabilities in the supercritical case and conditional expectation given non-extinction in the subcritical case.

Keywords

BRANCHING PROCESSES IN VARYING ENVIRONMENTSBRANCHING PROCESSES IN RANDOM ENVIRONMENTSFRACTIONAL LINEAR GENERATING FUNCTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 135 - 141
Copyright
Copyright © Applied Probability Trust 1975 

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References

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