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3 results

  • The advancing wave in a spatial birth process

  • H. E. Daniels
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 4 / December 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 689-701
    Print publication:
    December 1977

  • It is known that, in the deterministic model of a one-dimensional spatial linear birth process, a finite initial distribution of individuals develops into an advancing wave with the minimum velocity possible for such waves. In this paper, the spatial covariance density of the process is studied in the vicinity of a point moving outwards with a given velocity. Its behaviour casts doubt on the applicability of the deterministic result to individual realisations of the process.