On branching processes allowing immigration
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 9 (01) , 24-31
- https://doi.org/10.1017/s0021900200094651
Abstract
Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.Keywords
This publication has 4 references indexed in Scilit:
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- Functional equations and the Galton-Watson processAdvances in Applied Probability, 1969
- The Galton-Watson process with mean oneJournal of Applied Probability, 1967
- Transient Markov chains with stationary measuresProceedings of the American Mathematical Society, 1957