Integer-valued branching processes with immigration
- 1 December 1983
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 15 (4) , 713-725
- https://doi.org/10.2307/1427320
Abstract
The notion of self-decomposability for -valued random variables as introduced by Steutel and van Harn [10] and its generalization by van Harn, Steutel and Vervaat [5], are used to study the limiting behaviour of continuous-time Markov branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of random variables obeying a certain difference equation as studied by Vervaat [12] and their continuous-time counterpart considered by Wolfe [13]. An application in queueing theory is indicated. Furthermore, discrete-state analogues are given for results on stability in the processes studied by Wolfe, and for results on self-decomposability in supercritical branching processes by Yamazato [14].Keywords
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