On lower limits and equivalences for distribution tails of randomly stopped sums

Denis Denisov, Serguei Foss, Dmitry Korshunov

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

For a distribution F*t of a random sum St = ?1 + ... + ?t of i.i.d, random variables with a common distribution F on the half-line [0, 8), we study the limits of the ratios of tails F*t (x)/F (x) as x ? 8 (here, t is a counting random variable which does not depend on {? n}n= 1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes. © 2008 ISI/BS.

Original languageEnglish
Pages (from-to)391-404
Number of pages14
JournalBernoulli
Volume14
Issue number2
DOIs
Publication statusPublished - May 2008

Keywords

  • Convolution equivalence
  • Convolution tail
  • Lower limit
  • Randomly stopped sums
  • Subexponential distribution

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