Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T14:40:46.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Extinction of non-homogeneous Galton-Watson processes

Published online by Cambridge University Press:  14 July 2016

Miloslav Jirina
Miloslav Jirina*
Affiliation:
The Flinders University of South Australia
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

NON-HOMOGENEOUS GALTON–WATSON PROCESSESDEGENERACY OR EXTINCTION OF THE PROCESSNECESSARY AND SUFFICIENT CONDITIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 132 - 137
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Čistjakov, V. P. and Markova, N. P. (1962) On some theorems for inhomogeneous branching processes. Dokl. Akad. Nauk. SSSR 147, 317–320.Google Scholar
[2] Fearn, D. H. (1972) Galton-Watson processes with generation dependence. Proc. 6th Berkeley Symp. Math. Statist. Prob. 4, 159–172.Google Scholar
[3] Jagers, P. (1974) Galton-Watson processes in varying environments. J. Appl. Prob. 11, 174–178.Google Scholar