Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T14:59:21.043Z Has data issue: false hasContentIssue false
  • English
  • Français

The rates of growth of the Galton-Watson process in varying environment

Published online by Cambridge University Press:  14 July 2016

James H. Foster  and
Robert T. Goettge
James H. Foster*
Affiliation:
University of Denver
Robert T. Goettge*
Affiliation:
University of Colorado
*
*Now at Weber State College, Ogden, Utah.
**Now with The Aerospace Corporation.
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that a Galton-Watson process in varying environment, unlike a classical Galton-Watson process, can have an infinite (though at most countable) number of distinct rates of growth.

Keywords

GALTON–WATSON BRANCHING PROCESSVARYING ENVIRONMENTSRATES OF GROWTH
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 144 - 147
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] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Heidelberg.CrossRefGoogle Scholar
[2] Church, J. (1971) On infinite composition products of probability generating functions. Z. Wahrscheinlichkeitsth. 15, 243–256.Google Scholar
[3] Fearn, D. (1971) Galton–Watson processes with generation dependence. Proc. 6th Berkeley Symp. Math. Statist. Prob. 4, 159–172.Google Scholar
[4] Goettge, R. (1974) Limit theorems for the supercritical Galton-Watson process in varying environments. Math. Biosci., To appear.Google Scholar
[5] Jagers, P. (1974) Galton-Watson processes in varying environments. J. Appl. Prob. 11, 174–178.CrossRefGoogle Scholar
[6] Lindvall, T. (1974) Almost sure convergence of branching processes in varying and random environments. Ann. Prob. 2, 344–346.Google Scholar