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A model for random instantaneous growth on an interval

Published online by Cambridge University Press:  14 July 2016

M. P. Quine
M. P. Quine*
Affiliation:
University of Sydney
*
∗ Postal address: Department of Mathematical Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

Points arrive in succession on an interval and immediately ‘cover' a region of length ½ to each side (less if they are close to the boundary or to a covered part). The location of a new point is uniformly distributed on the uncovered parts. We study the mean and variance of the total number of points ever formed, in particular as a → 0, in which case we also establish asymptotic normality.

Keywords

RANDOM GROWTHCOVERAGEMOMENTSCENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 529 - 538
Copyright
Copyright © Applied Probability Trust 1991 

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References

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