Integer-valued branching processes with immigration

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

Integer-valued branching processes with immigration

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

Mathematics and Computer Science

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Abstract

The notion of self-decomposability for N0-valued rv's as introduced by Steutel and van Harn [8] and its generalization by van Ham, Steutel and Vervaat [4], are used to study the limiting behaviour of continuous-time branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of rv's obeying a certain difference equation as studied by Vervaat [10] and their continuous-time counterpart considered by Wolfe [11]. 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 [12].

Original language	English
Place of Publication	Eindhoven
Publisher	Technische Hogeschool Eindhoven
Number of pages	20
Publication status	Published - 1982

Publication series

Name	Memorandum COSOR
Volume	8218
ISSN (Print)	0926-4493

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abstract = "The notion of self-decomposability for N0-valued rv's as introduced by Steutel and van Harn [8] and its generalization by van Ham, Steutel and Vervaat [4], are used to study the limiting behaviour of continuous-time branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of rv's obeying a certain difference equation as studied by Vervaat [10] and their continuous-time counterpart considered by Wolfe [11]. 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 [12].",

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