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1 results

  • Series expansions for the properties of a birth process of controlled variability

  • D. R. Cox, V. Isham
  • Journal:
    Journal of Applied Probability / Volume 15 / Issue 3 / September 1978
    Published online by Cambridge University Press:
    14 July 2016, pp. 610-616
    Print publication:
    September 1978

  • A birth process is studied in which the birth rate at any time is a function of the difference between the current population size and a target corresponding to unit growth rate. If this controlling function is a decreasing function of its argument a stabilizing effect is to be expected. By supposing that the controlling function varies very slowly, series expansions for the properties of the process are obtained, the leading term corresponding to a diffusion approximation. The sequence of births considered as a point process of controlled variability is examined and approximations to the interval distribution and covariance density obtained.