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A note on a model for restoring a destroyed region

Part of: Geometric probability and stochastic geometry Limit theorems

Published online by Cambridge University Press:  14 July 2016

J. Hüsler
J. Hüsler*
Affiliation:
University of Bern
*
∗Postal address: Department of Mathematical Statistics, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland.
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Abstract

We introduce a model for the healing process of a destroyed region and use some relations to the coverage models. The restoring model depends on the region which is hit n times at random. Each random part of the region which is destroyed is restored at a certain fixed speed, but the restoring process may start after a random delay. We focus mainly on the total healing time until the whole region is restored, and analyse its limit distribution as n tends to ∞. The dependence of this limit distribution on the different ingredients is of interest. We consider two cases with different geometrical influence. One case is restricted to a one-dimensional region, that means the circumference of a circle or the unit interval as region. The results follow from extreme value theory. We discuss also some particular cases and examples.

Keywords

COVERAGE MODELSWOUND HEALINGREGENERATION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 756 - 767
Copyright
Copyright © Applied Probability Trust 1995 

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