The critical branching process with immigration stopped at zero
- 1 March 1985
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 22 (1) , 223-227
- https://doi.org/10.2307/3213762
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
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