Extinction of non-homogeneous Galton-Watson processes
- 1 March 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (01) , 132-137
- https://doi.org/10.1017/s0021900200049081
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
This publication has 1 reference indexed in Scilit:
- Galton-Watson processes in varying environmentsJournal of Applied Probability, 1974