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A general linear birth and growth model

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

M. P. Quine  and
W. Szczotka
M. P. Quine*
Affiliation:
University of Sydney
W. Szczotka*
Affiliation:
University of Wrocław
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: malcolmq@maths.usyd.edu.au
∗∗ Postal address: Institute of Mathematics, Wrocław University, 50-384 Wrocław, Poland.
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Abstract

We consider a birth and growth model where points (‘seeds’) arrive on a line randomly in time and space and proceed to ‘cover’ the line by growing at a uniform rate in both directions until an opposing branch is met; points which arrive on covered parts of the line do not contribute to the process. Existing results concerning the number of seeds assume that points arrive according to a Poisson process, homogeneous on the line, but possibly inhomogeneous in time. We derive results under less stringent assumptions, namely that the arrival process be a stationary simple point process.

Keywords

Birth and growth on ℝnumber of seedslimit resultsstationary simple point process

MSC classification

Primary: 60G55: Point processes
Secondary: 60F17: Functional limit theorems; invariance principles

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 4 , December 2000 , pp. 1027 - 1050
Copyright
Copyright © Applied Probability Trust 2000 

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