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

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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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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
Divisions: Faculty of Engineering and Natural Sciences
Faculty of Engineering and Natural Sciences > Academic programs > Manufacturing Systems Eng.
Depositing User: Hans Frenk
Date Deposited: 28 Feb 2011 14:21
Last Modified: 26 Apr 2022 08:45
URI: https://research.sabanciuniv.edu/id/eprint/16382

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