Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T17:46:21.543Z Has data issue: false hasContentIssue false
  • English
  • Français

On a result of Rubin and Vere-Jones concerning subcritical branching processes

Published online by Cambridge University Press:  14 July 2016

Fred M. Hoppe
Fred M. Hoppe*
Affiliation:
University of Alberta, Edmonton
Get access Rights & Permissions [Opens in a new window]

Abstract

If a subcritical Galton-Watson process is initiated with an arbitrary mass distribution, then it is known that under certain conditions proper conditional limit distributions exist, depending on a single parameter. It is shown here that there is a one-to-one correspondence between these distributions and those arising from the process with a linear offspring probability generating function.

Keywords

GALTON-WATSON PROCESSYAGLOM LIMITREGULAR VARIATIONLINEARIZATIONFUNCTIONAL EQUATIONSCONVEXITYGENERATING FUNCTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 804 - 808
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] Heathcote, C. R., Seneta, E. and Vere-Jones, D. (1967) A refinement of two theorems in the theory of branching processes. Theor. Prob. Appl. 12, 341–346.Google Scholar
[2] Hoppe, F. (1975a) Functional Equations with Applications to Multitype Galton-Watson Branching Processes. Ph.D. dissertation, Princeton University.Google Scholar
[3] Hoppe, F. (1975b) Stationary measures for multitype branching processes. J. Appl. Prob. 12, 219–227.CrossRefGoogle Scholar
[4] Rubin, H. and Vere-Jones, D. (1968) Domains of attraction for the subcritical Galton-Watson process. J. Appl. Prob. 5, 216–219.Google Scholar
[5] Seneta, E. (1971) On invariant measures for simple branching processes. J. Appl. Prob. 8, 43–51.CrossRefGoogle Scholar
[6] Seneta, E. and Vere-Jones, D. (1966) On quasi-stationary distributions in discrete time Markov chains with a denumerable infinity of states. J. Appl. Prob. 3, 403–434.Google Scholar