### Asymptotic behavior of tail and local probabilities for sums of subexponential random variables

Kai W. Ng and Qihe Tang
Source: J. Appl. Probab. Volume 41, Number 1 (2004), 108-116.

#### Abstract

Let {Xk, k ≥ 1} be a sequence of independently and identically distributed random variables with common subexponential distribution function concentrated on (-∞,∞), and let τ be a nonnegative and integer-valued random variable with a finite mean and which is independent of the sequence {Xk, k ≥ 1}. This paper investigates asymptotic behavior of the tail probabilities P(· > x) and the local probabilities P(x < · ≤ x + h) of the quantities X(n) = max0≤knXk, Sn = ∑k=0nXk and S(n) = max0≤knSk for n ≥ 1, and their randomized versions X(τ), Sτ and S(τ), where X0 = 0 by convention and h > 0 is arbitrarily fixed.

First Page:
Primary Subjects: 60G50
Secondary Subjects: 62E20
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1077134671
Digital Object Identifier: doi:10.1239/jap/1077134671
Mathematical Reviews number (MathSciNet): MR2036275
Zentralblatt MATH identifier: 02103349

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