A linear random growth model
- 1 September 1990
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 27 (3) , 499-509
- https://doi.org/10.2307/3214536
Abstract
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.Keywords
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