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1 results

  • A limit theorem for the tails of discrete infinitely divisible laws with applications to fluctuation theory

  • Paul Embrechts, John Hawkes
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 32 / Issue 3 / June 1982
    Published online by Cambridge University Press:
    09 April 2009, pp. 412-422
    Print publication:
    June 1982
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  • Suppose that (pn) is an infinitely divisible distribution on the non-negative integers having Lévy measure (vn). In this paper we derive a necessary and sufficient condition for the existence of the limit limn→∞ pn/vn. We also derive some other results on the asymptotic behaviour of the sequence (Pn) and apply some of our results to the theory of fluctuations of random walks. We obtain a necessary and sufficient condition for the first positive ladder epoch to belong to the domain of attraction of a spectrally positive stable law with index α, α ∈ (1,2).