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Siberian Mathematical Journal

, Volume 47, Issue 4, pp 779–786 | Cite as

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

  • V. V. Shneer
Article

Abstract

Let {i} i=1 be a sequence of independent identically distributed nonnegative random variables, S n = ξ1 + ⋯ +ξn. Let Δ = (0, T] and x + Δ = (x, x + T]. We study the ratios of the probabilities P(S n ε x + Δ)/P1 ε x + Δ) for all n and x. The estimates uniform in x for these ratios are known for the so-called Δ-subexponential distributions. Here we improve these estimates for two subclasses of Δ-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 ≤ ∞. Also, a characterization of the class LC is given.

Keywords

subexponential distribution locally subexponential distribution sums of random variables estimates for interval probabilities 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. V. Shneer
    • 1
  1. 1.Heriot-Watt UniversityEdinburgh ScotlandUK

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