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

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  • Geluk, J.L.
  • Frenk, J.B.G.

Abstract

Let X1,X2,...Xn be independent and identically distributed (i.i.d.) non-negative random variables with a common distribution function (d.f.) F with unbounded support and . We show that for a large class of heavy tailed random variables with a finite variance the renewal function U satisfies as x-->[infinity].

Suggested Citation

  • Geluk, J.L. & Frenk, J.B.G., 2011. "Renewal theory for random variables with a heavy tailed distribution and finite variance," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 77-82, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:77-82
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    References listed on IDEAS

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    1. Ney, Peter, 1981. "A refinement of the coupling method in renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 11(1), pages 11-26, March.
    2. Asmussen, Søren & Kalashnikov, Vladimir & Konstantinides, Dimitrios & Klüppelberg, Claudia & Tsitsiashvili, Gurami, 2002. "A local limit theorem for random walk maxima with heavy tails," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 399-404, February.
    3. Geluk, Jaap, 2009. "Some closure properties for subexponential distributions," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1108-1111, April.
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    Cited by:

    1. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    2. Losidis, Sotirios & Politis, Konstadinos, 2017. "A two-sided bound for the renewal function when the interarrival distribution is IMRL," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 164-170.

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