On the subcritical Bellman-Harris process with immigration
- 1 December 1974
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (4) , 652-668
- https://doi.org/10.2307/3212549
Abstract
Some necessary and sufficient conditions are found for the existence of a proper non-degenerate limiting distribution for a Bellman-Harris age-dependent branching process with a compound renewal immigration component. A number of these results are applicable to the batch arrivalGI/G/∞queueing process. Some aspects of the situation when there is no such limiting distribution are considered. The situation when the immigration component is a nonhomogeneous compound Poisson process is briefly considered.Keywords
This publication has 13 references indexed in Scilit:
- Limit theorems for an age-dependent branching process with immigrationMathematical Biosciences, 1972
- On branching processes allowing immigrationJournal of Applied Probability, 1972
- On branching processes allowing immigrationJournal of Applied Probability, 1972
- Branching ProcessesPublished by Springer Nature ,1972
- Some results for the supercritical branching process with immigrationMathematical Biosciences, 1971
- Strong renewal theorems with infinite meanTransactions of the American Mathematical Society, 1970
- Age-Dependent Branching Processes Allowing ImmigrationTheory of Probability and Its Applications, 1968
- The Galton-Watson process with mean oneJournal of Applied Probability, 1967
- The Galton-Watson process with mean oneJournal of Applied Probability, 1967
- The Probability in the Tail of a DistributionThe Annals of Mathematical Statistics, 1963