Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T12:09:33.179Z Has data issue: false hasContentIssue false
  • English
  • Français

Branching processes with random absorbing processes

Published online by Cambridge University Press:  14 July 2016

F. Thomas Bruss
F. Thomas Bruss*
Affiliation:
University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

A discrete Galton–Watson process is modified by an absorbing process, which, within each generation, eliminates a subset of the living particles without leaving offspring. The absorbing process will be only roughly specified by its expected efficiency on the associated process. We give a sharp sufficient condition for the joint process to be extinguished with probability one and give, after an easy generalization, an example for possible biomedical applications.

Keywords

BRANCHING PROCESSABSORPTIONEXTINCTION PROBABILITYBOUNDED POPULATION GROWTH
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 54 - 64
Copyright
Copyright © Applied Probability Trust 1978 

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] Cherniavsky, E. A. and Taylor, H. M. (1972) Control of a lethal growth process. Math. Biosci. 13, 235–252.CrossRefGoogle Scholar
[2] Costello, W. G. and Taylor, H. M. (1973) Mathematical models of the sterile male technique of insect control. Proceedings of NATO Conference on Mathematical Analysis of Decison Problems in Ecology, Istanbul, 129–173.Google Scholar
[3] Dietz, K. (1973) Simulation models for genetic control alternatives. In Lecture Notes in Biomathematics 5, Springer-Verlag, Berlin, 299–317.Google Scholar
[4] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[5] Kaplan, N., Sudbury, A. and Nilsen, T. (1975) A branching process with disasters. J. Appl. Prob. 12, 47–59.CrossRefGoogle Scholar
[6] Neuts, M. F. (1968) Controlling a lethal growth process. Math. Biosci. 2, 41–54.CrossRefGoogle Scholar
[7] Schuh, H.-J. (1976) A condition for the extinction of a branching process with an absorbing lower boundary. J. Math. Biol. 3, 271–287.CrossRefGoogle Scholar
[8] Turnbull, B. W. (1973) Inequalities for branching processes. Ann. Prob. 1, 457–474.Google Scholar
[9] Zubkov, A. M. (1970) A degeneracy condition for a bounded branching process (In Russian). Mat. Zametki 8, 9–18. English translation: Math. Notes 8, 472–477.Google Scholar