Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-19T14:58:21.076Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Quine, M. P. and Robinson, J. (1990) A linear random growth model. J. Appl. Prob. 27, 499–509.CrossRefGoogle Scholar
Shimizu, R. and Davies, L. (1981) General characterization theorems for the Weibull and the stable distributions. Sankhya A43, 282–310.Google Scholar
Vanderbei, R. J. and Shepp, L. A. (1988) A probabilistic model for the time to unravel a strand of DNA. Commun. Statist.-Stoch. Models 4, 299–314.CrossRefGoogle Scholar