Hostname: page-component-6898cfcb55-th4rj Total loading time: 0 Render date: 2026-11-12T03:40:47.170Z Has data issue: false hasContentIssue false
  • English
  • Français

A fixed-point property for Galton–Watson processes with generation dependence

Published online by Cambridge University Press:  14 July 2016

Dean H. Fearn
Dean H. Fearn*
Affiliation:
California State University
*
∗Postal address: Department of Statistics, California State University, Hayward, CA 94542, U.S.A.
Get accessRights & Permissions [Opens in a new window]

Abstract

Conditions for the non-sure extinction of Galton-Watson processes with generation dependence are obtained. Also a condition is given for such processes to have a strictly increasing probability generating function.

Keywords

BRANCHING PROCESSESEXTINCTION PROBABILITYVARYING ENVIRONMENTGENERATION DEPENDENCEFIXED POINT FOR A FAMILY OF PROBABILITY GENERATING FUNCTIONS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981, pp. 514 - 519
Copyright
Copyright © Applied Probability Trust 

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.)

Article purchase

Temporarily unavailable

References

[1] Church, J. D. (1971) On infinite composition of probability generating functions. Z. Wahrscheinlichkeitsth. 19, 243–256.Google Scholar
[2] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
[3] Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
[4] Jirina, M. (1976) Extinction of non-homogeneous Galton-Watson processes. J. Appl. Prob. 13, 132–137.Google Scholar