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1 results

  • A note on a model for restoring a destroyed region

  • Part of
  • J. Hüsler
  • Journal:
    Journal of Applied Probability / Volume 32 / Issue 3 / September 1995
    Published online by Cambridge University Press:
    14 July 2016, pp. 756-767
    Print publication:
    September 1995

  • 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.