Integer-valued branching processes with immigration

F.W. Steutel, W. Vervaat, S.J. Wolfe

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

The notion of self-decomposability for N0-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].
Original languageEnglish
Pages (from-to)713-725
Number of pages13
JournalAdvances in Applied Probability
Volume15
Issue number4
DOIs
Publication statusPublished - 1983

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