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A linear random growth model

Published online by Cambridge University Press:  14 July 2016

M. P. Quine  and
J. Robinson
M. P. Quine
Affiliation:
University of Sydney
J. Robinson*
Affiliation:
University of Sydney
*
∗Postal address for both authors: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

Points start to form on an ‘uncovered' unit interval according to a Poisson process with parameter λ. From newly formed points a covering region grows in both directions at velocity v, while new points continue to form on uncovered parts of the interval. Eventually the whole interval will be covered. Let N ≧ 1 denote the total number of points formed. We derive integral expressions for E(N) and Var(N) and give precise asymptotic expressions for these moments as ρ = λ/v →∞. Asymptotic normality of N is also established.

Keywords

POISSON PROCESS WITH INHIBITIONGROWTHMOMENTSCENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 499 - 509
Copyright
Copyright © Applied Probability Trust 1990 

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