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

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1980 

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References

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