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On the extinction times of varying and random environment branching processes

Published online by Cambridge University Press:  14 July 2016

Alan Agresti
Alan Agresti*
Affiliation:
Department of Statistics, University of Florida
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Abstract

Bounds are derived for the probability of extinction by the nth generation for a branching process in a varying environment. From these bounds, necessary and sufficient conditions are established for such a process to become extinct with probability one. The extinction time of a random environment branching process in which the environmental random variables are independent but not necessarily identically distributed is stochastically bounded by the extinction times of two varying environment processes.

Keywords

BRANCHING PROCESSESVARYING ENVIRONMENTRANDOM ENVIRONMENTEXTINCTION TIMEPROBABILITY OF EXTINCTIONPOISSON OFFSPRING
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 39 - 46
Copyright
Copyright © Applied Probability Trust 1975 

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References

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