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

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 {X_k, 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 {X_k, 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) = max_0≤k≤nX_k, S_n = ∑_k=0ⁿX_k and S_(n) = max_0≤k≤nS_k for n ≥ 1, and their randomized versions X_(τ), S_τ and S_(τ), where X₀ = 0 by convention and h > 0 is arbitrarily fixed.

First Page: Show

Primary Subjects: 60G50

Secondary Subjects: 62E20

Keywords: Asymptotics; local probability; partial sum; subexponentiality; tail probability

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Links and Identifiers

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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