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1 results

  • The extinction time of a birth, death and catastrophe process and of a related diffusion model

  • P. J. Brockwell
  • Journal:
    Advances in Applied Probability / Volume 17 / Issue 1 / March 1985
    Published online by Cambridge University Press:
    01 July 2016, pp. 42-52
    Print publication:
    March 1985

  • The distribution of the extinction time for a linear birth and death process subject to catastrophes is determined. The catastrophes occur at a rate proportional to the population size and their magnitudes are random variables having an arbitrary distribution with generating function d(·). The asymptotic behaviour (for large initial population size) of the expected time to extinction is found under the assumption that d(.) has radius of convergence greater than 1. Corresponding results are derived for a related class of diffusion processes interrupted by catastrophes with sizes having an arbitrary distribution function.