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Some properties of continuous-state branching processes, with applications to Bartoszyński’s virus model

Published online by Cambridge University Press:  01 July 2016

Anthony G. Pakes  and
A. C. Trajstman
Anthony G. Pakes*
Affiliation:
University of Western Australia
A. C. Trajstman*
Affiliation:
CSIRO Division of Mathematics and Statistics
*
∗Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
∗∗ Postal address: CSIRO Division of Mathematics and Statistics, Private Bag 10, Clayton, VIC 3168, Australia.
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Abstract

It is known that Bartoszyński’s model for the growth of rabies virus in an infected host is a continuous branching process. We show by explicit construction that any such process is a randomly time-transformed compound Poisson process having a negative linear drift.

This connection is exploited to obtain limit theorems for the population size and for the jump times in the rabies model. Some of these results are obtained in a more general context wherein the compound Poisson process is replaced by a subordinator.

Keywords

CONTINUOUS BRANCHING PROCESSLÉVY PROCESSLIMIT THEOREMS
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 23 - 41
Copyright
Copyright © Applied Probability Trust 1985 

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