Estimates for interval probabilities of the sums of random variables with locally subexponential distributions

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Abstract

Let {i} i=1 be a sequence of independent identically distributed nonnegative random variables, S n = ?1 + ? +?n. Let ? = (0, T] and x + ? = (x, x + T]. We study the ratios of the probabilities P(S n e x + ?)/P(? 1 e x + ?) for all n and x. The estimates uniform in x for these ratios are known for the so-called ?-subexponential distributions. Here we improve these estimates for two subclasses of ?-subexponential distributions; one of them is a generalization of the well-known class LC to the case of the interval (0, T] with an arbitrary T 8. Also, a characterization of the class LC is given. © 2006 Springer Science+Business Media, Inc.

Original languageEnglish
Pages (from-to)779-786
Number of pages8
JournalSiberian Mathematical Journal
Volume47
Issue number4
DOIs
Publication statusPublished - Jul 2006

Keywords

  • Estimates for interval probabilities
  • Locally subexponential distribution
  • Subexponential distribution
  • Sums of random variables

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