Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

Søren Asmussen, Serguei Foss, Dmitry Korshunov

Research output: Contribution to journalArticlepeer-review

89 Citations (Scopus)


We study distributions F on [0, 8) such that for some T = 8, F*2(x, x+T] ~ 2F(x, x+T]. The case T = 8 corresponds to F being subexponential, and our analysis shows that the properties for T < 8 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
Number of pages30
JournalJournal of Theoretical Probability
Issue number2
Publication statusPublished - Apr 2003


  • Distribution tails
  • Local probabilities
  • Subexponential distributions
  • Sums of independent random variables


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