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A note on models using the branching process with immigration stopped at zero

Published online by Cambridge University Press:  14 July 2016

E. Seneta  and
S. Ta Varé
E. Seneta*
Affiliation:
University of Sydney
S. Ta Varé*
Affiliation:
Colorado State University
*
∗ Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
∗∗ Postal address: Department of Statistics, Colorado State University, Fort Collins CO 80523, U.S.A.
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Abstract

The Galton-Watson process with immigration which is time-homogeneous but not permitted when the process is in state 0 (so that this state is absorbing) is briefly studied in the subcritical and supercritical cases. Results analogous to those for the ordinary Galton-Watson process are found to hold. Partly-new techniques are required, although known end-results on the standard process with and without immigration are used also. In the subcritical case a new parameter is found to be relevant, replacing to some extent the criticality parameter.

Keywords

GALTON-WATSON PROCESSIMMIGRATIONSUBCRITICALSUPERCRITICALRENEWAL EQUATIONEXTINCTION-TIME DISTRIBUTIONPLASMIDS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 11 - 18
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research carried out while this author was visiting Colorado State University.

References

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