Abstract
In the paper the problem of the extinction of non-homogeneous Galton-Watson processes with one type of particle is studied. It is proved that the process becomes extinct if the expectations of the process do not converge to a limit (finite or infinite). If the expectations have a finite limit, then simple necessary and sufficient conditions for the extinction are proved. The general case remains open; however two more sufficient conditions which are also necessary under some restrictions are given.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference3 articles.
1. Galton-Watson processes with generation dependence;Fearn;Proc. 6th Berkeley Symp. Math. Statist. Prob.,1972
2. Galton-Watson processes in varying environments
3. On some theorems for inhomogeneous branching processes;Čistjakov;Dokl. Akad. Nauk. SSSR,1962
Cited by
19 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A unifying approach to branching processes in a varying environment;Journal of Applied Probability;2020-03
2. The segregated $\Lambda$-coalescent;The Annals of Probability;2015-03-01
3. Bibliography;Introduction to Stochastic Models;2013-04-23
4. Obituary: Miloslav Jiřina;Journal of Applied Probability;2012-06
5. Obituary:Miloslav Jiřina;Journal of Applied Probability;2012-06