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1 results

  • A linear random growth model

  • M. P. Quine, J. Robinson
  • Journal:
    Journal of Applied Probability / Volume 27 / Issue 3 / September 1990
    Published online by Cambridge University Press:
    14 July 2016, pp. 499-509
    Print publication:
    September 1990

  • 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.