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The critical branching process with immigration stopped at zero

Published online by Cambridge University Press:  14 July 2016

B. Gail Ivanoff  and
E. Seneta
B. Gail Ivanoff*
Affiliation:
University of Ottawa
E. Seneta*
Affiliation:
University of Sydney
*
∗Postal address: Department of Mathematics, University of Ottawa, Ont., Canada K1N 9B4.
∗∗Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

Limit theorems for the Galton–Watson process with immigration (BPI), where immigration is not permitted when the process is in state 0 (so that this state is absorbing), have been studied for the subcritical and supercritical cases by Seneta and Tavaré (1983). It is pointed out here that, apart from a change of context, the corresponding theorem in the critical case has been obtained by Vatutin (1977). Extensions which follow from a more general form of initial distribution are sketched, including a new form of limit result (7).

Keywords

EXTINCTION-TIME DISTRIBUTIONREGULARLY VARYING FUNCTIONABELIAN–TAUBERIAN
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 223 - 227
Copyright
Copyright © Applied Probability Trust 1985 

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