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2 results

  • On the extinction time distribution of a branching process in varying environments

  • Tetsuo Fujimagari
  • Journal:
    Advances in Applied Probability / Volume 12 / Issue 2 / June 1980
    Published online by Cambridge University Press:
    01 July 2016, pp. 350-366
    Print publication:
    June 1980

  • The extinction time distributions of a class of branching processes in varying environments are considered. We obtain (i) sufficient conditions for the extinction probability q = 1 or q < 1; (ii) asymptotic formulae for the tail probability of the extinction time if q = 1; and (iii) upper bounds for 1 – q if q < 1. To derive these results, we give upper and lower bounds for the tail probability of the extinction time. For the proofs, we use a method that compares probability generating functions with fractional linear generating functions.