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On the extinction time distribution of a branching process in varying environments

Published online by Cambridge University Press:  01 July 2016

Tetsuo Fujimagari
Tetsuo Fujimagari*
Affiliation:
Kanazawa University
*
∗Postal address: Kanazawa University, College of Liberal Arts, 1-1 Marunouchi, Kanazawa 920, Japan.
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Abstract

The extinction time distributions of a class of branching processes in varying environments are considered. We obtain (i) sufficient conditions for the extinction probability q = 1 or q < 1; (ii) asymptotic formulae for the tail probability of the extinction time if q = 1; and (iii) upper bounds for 1 – q if q < 1. To derive these results, we give upper and lower bounds for the tail probability of the extinction time. For the proofs, we use a method that compares probability generating functions with fractional linear generating functions.

Keywords

BRANCHING PROCESSVARYING ENVIRONMENTSEXTINCTION TIME DISTRIBUTIONEXTINCTION PROBABILITYFRACTIONAL LINEAR FUNCTIONFRACTIONAL LINEAR GENERATING FUNCTION
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 2 , June 1980 , pp. 350 - 366
Copyright
Copyright © Applied Probability Trust 1980 

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References

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