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1 results

  • The extinction time of a general birth and death process with catastrophes

  • P. J. Brockwell
  • Journal:
    Journal of Applied Probability / Volume 23 / Issue 4 / December 1986
    Published online by Cambridge University Press:
    24 August 2016, pp. 851-858
    Print publication:
    December 1986

  • The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfy λ0 = 0, λ j > 0 for each j > 0, and . Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λ j = jλ, µj = jμ) with catastrophes of several different types.