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. 7782. ISSN 01677152
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Official URL: http://dx.doi.org/10.1016/j.spl.2010.09.021
Abstract
Let X1, X2,... Xn be independent and identically distributed (i.i.d.) nonnegative 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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Renewal theory for random variables with a heavy tailed distribution and finite variance. (deposited 03 Nov 2010 16:53)
 Renewal theory for random variables with a heavy tailed distribution and finite variance. (deposited 28 Feb 2011 14:21) [Currently Displayed]