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1 results

  • A general linear birth and growth model

  • Part of
  • M. P. Quine, W. Szczotka
  • Journal:
    Advances in Applied Probability / Volume 32 / Issue 4 / December 2000
    Published online by Cambridge University Press:
    01 July 2016, pp. 1027-1050
    Print publication:
    December 2000

  • We consider a birth and growth model where points (‘seeds’) arrive on a line randomly in time and space and proceed to ‘cover’ the line by growing at a uniform rate in both directions until an opposing branch is met; points which arrive on covered parts of the line do not contribute to the process. Existing results concerning the number of seeds assume that points arrive according to a Poisson process, homogeneous on the line, but possibly inhomogeneous in time. We derive results under less stringent assumptions, namely that the arrival process be a stationary simple point process.