On the extinction time distribution of a branching process in varying environments
- 1 June 1980
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 12 (2) , 350-366
- https://doi.org/10.2307/1426601
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
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