Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T19:48:43.569Z Has data issue: false hasContentIssue false
  • English
  • Français

The condition for extinction by probability one in a birth, death and migration process

Published online by Cambridge University Press:  01 July 2016

Inge S. Helland
Inge S. Helland*
Affiliation:
University of Bergen
Get access Rights & Permissions [Opens in a new window]

Abstract

For the n-dimensional birth, death and migration process with constant rates, Aksland (1975) found a necessary and sufficient condition that the extinction-probability be one. This condition is translated into the form of direct relations between the parameters of the model.

Keywords

BIRTHDEATH AND MIGRATIONEXTINCTION IN MEAN AND ALMOST SURELY
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 61 - 65
Copyright
Copyright © Applied Probability Trust 1975 

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

Aksland, M. (1975) A birth, death and migration process with immigration. Adv. Appl. Prob. 7, 44–60 CrossRefGoogle Scholar
Gantmacher, F. R. (1959) The Theory of Matrices. Vol. II. Chelsea Publishing Company, New York.Google Scholar
Marcus, M. and Minc, H. (1964) A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston.Google Scholar
Renshaw, E. (1972) Birth, death and migration processes. Biometrika 59, 49–60.CrossRefGoogle Scholar