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

Part of: Stochastic processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Kai W. Ng  and
Qihe Tang
Kai W. Ng*
Affiliation:
University of Hong Kong
Qihe Tang*
Affiliation:
University of Amsterdam
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong. Email address: [email protected]
∗∗ Postal address: Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands. Email address: [email protected]
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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 and for n ≥ 1, and their randomized versions X (τ), S τ and S (τ), where X 0 = 0 by convention and h > 0 is arbitrarily fixed.

Keywords

Asymptoticslocal probabilitypartial sumsubexponentialitytail probability

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 108 - 116
Copyright
Copyright © Applied Probability Trust 2004 

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