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Near-constancy phenomena in branching processes

Published online by Cambridge University Press:  24 October 2008

J. D. Biggins  and
N. H. Bingham
J. D. Biggins
Affiliation:
Department of Probability and Statistics, The University of Sheffield, P.O. Box 597, Sheffield 510 2UN
N. H. Bingham
Affiliation:
Mathematical Department, Royal Holloway and Bedford New College, Egham Hill, Egham, Surrey TW2O OEX
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Extract

The occurrence of certain ‘near-constancy phenomena’ in some aspects of the theory of (simple) branching processes forms the background for the work below. The problem arises out of work by Karlin and McGregor [8, 9]. A detailed study of the theoretical and numerical aspects of the Karlin–McGregor near-constancy phenomenon was given by Dubuc[7], and considered further by Bingham[4]. We give a new approach which simplifies and generalizes the results of these authors. The primary motivation for doing this was the recent work of Barlow and Perkins [3], who observed near-constancy in a framework not immediately covered by the results then known.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 545 - 558
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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