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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
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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 

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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