Asymptotics for sums of random variables with local subexponential behaviour

Sören Asmussen, S Foss, D Korshunov

Research output: Contribution to journalArticlepeer-review

80 Citations (SciVal)

Abstract

We study distributions F on [0, infinity) such that for some T less than or equal to infinity F*(2)(x, x + T] similar to 2F(x, x + T]. The case T = infinity corresponds to F being subexponential, and our analysis shows that the properties for T < &INFIN; are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.
Original languageEnglish
Pages (from-to)489-518
JournalJournal of Theoretical Probability
Volume16
Issue number2
DOIs
Publication statusPublished - 2003

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • local probabilities
  • distribution tails
  • Sums of independent random variables
  • subexponential distributions

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