Bounds for the extinction probability of a simple branching process
- 1 March 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (01) , 9-16
- https://doi.org/10.1017/s0021900200048956
Abstract
The extinction probability q of a supercritical simple branching process is well known to be less than unity. Intuitively, it is apparent that when the offspring mean is close to one, so, usually, will q be. This notion is made rigorous, and simple bounds are given for q in terms of the second and third factorial moments, which are applicable when the offspring mean is close to unity. A comparison is made of various upper bounds for q. The note contains some numerical examples.Keywords
This publication has 2 references indexed in Scilit:
- Heavy traffic approximations for the Galton-Watson processAdvances in Applied Probability, 1971
- Bounds for moment generating functions and for extinction probabilitiesJournal of Applied Probability, 1966