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Renewal theory for random variables with a heavy tailed distribution and finite variance

Geluk, Jaap J.L and Frenk , Hans J.B.G. (2011) Renewal theory for random variables with a heavy tailed distribution and finite variance. Statistics and Probability Letters, 81 (1). pp. 77-82. ISSN 0167-7152

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Official URL: http://dx.doi.org/10.1016/j.spl.2010.09.021

Abstract

Let X-1, X-2,... X-n be independent and identically distributed (i.i.d.) non-negative random variables with a common distribution function (d.f.) F with unbounded support and EX12 < infinity. We show that for a large class of heavy tailed random variables with a finite variance the renewal function U satisfies U(x) - x/mu - mu(2)/2 mu(2) similar to -1/mu x integral(infinity)(x) integral(infinity)(s) (1 - F(u))duds as x -> infinity.

Item Type:Article
Uncontrolled Keywords:Renewal function, Subexponentiality, Integrated tail, Dominated Variation
Subjects:Q Science > QA Mathematics
ID Code:16382
Deposited By:Hans Frenk
Deposited On:28 Feb 2011 14:21
Last Modified:20 Nov 2012 21:04

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