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Integer-valued branching processes with immigration

Published online by Cambridge University Press:  01 July 2016

F. W. Steutel ,
W. Vervaat  and
S. J. Wolfe
F. W. Steutel*
Affiliation:
University of Technology, Eindhoven
W. Vervaat*
Affiliation:
Catholic University, Nijmegen
S. J. Wolfe*
Affiliation:
University of Delaware
*
∗Postal address: Department of Mathematics, University of Technology, 5600 MB Eindhoven, The Netherlands.
∗∗Postal address: Mathematisch Instituut, Katholieke Universiteit, Toernooiveld, 6525 ED Nijmegen. The Netherlands.
∗∗∗Postal address: Sharp Laboratory, University of Delaware, Newark, DE 19711, U.S.A. Supported by NSF grants MCS 78-02566 and MCS 80-26546.
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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

STOCHASTIC DIFFERENCE EQUATIONSTOCHASTIC DIFFERENTIAL EQUATIONSELF-DECOMPOSABLE (CLASS L)STABLE
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 4 , December 1983 , pp. 713 - 725
Copyright
Copyright © Applied Probability Trust 1983 

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References

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