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1 results

  • Large deviations in the supercritical branching process

  • Part of
  • J. D. Biggins, N. H. Bingham
  • Journal:
    Advances in Applied Probability / Volume 25 / Issue 4 / December 1993
    Published online by Cambridge University Press:
    01 July 2016, pp. 757-772
    Print publication:
    December 1993

  • The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.