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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 178–182 (Mi tvp3381)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Second order renewal theorem in the finite-means case

A. Baltrūnasa, E. Omeyb

a Institute of Mathematics and Informatics
b Hogeschool-Universiteit Brussel

Abstract: Let $F$ be a distribution function (d.f.) on $(0, \infty )$ and let $U$ be the renewal function associated with $F$. If $F$ has a finite first moment $\mu$, then it is well known that $U(t)$ asymptotically equals $t/\mu$. It is also well known that $U(t)-t/\mu $ asymptotically behaves as $S(t)/\mu, $ where $S$ denotes the integral of the integrated tail distribution $F_1$ of $F$. In this paper we discuss the rate of convergence of $U(t)-t/\mu -S(t)/\mu $ for a large class of distribution functions. The estimate improves earlier results of Geluk, Teugels, and Embrechts and Omey.

Keywords: renewal function, subexponential distributions, regular variation, $O$-regular variation.

DOI: https://doi.org/10.4213/tvp3381

Full text: PDF file (555 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 127–132

Bibliographic databases:

Received: 17.12.1999
Language:

Citation: A. Baltrūnas, E. Omey, “Second order renewal theorem in the finite-means case”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 178–182; Theory Probab. Appl., 47:1 (2003), 127–132

Citation in format AMSBIB
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\by A.~Baltr{\=u}nas, E.~Omey
\paper Second order renewal theorem in the finite-means case
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 1
\pages 178--182
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1978707}
\zmath{https://zbmath.org/?q=an:1036.60077}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 127--132
\crossref{https://doi.org/10.1137/S0040585X97979561}
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  • https://doi.org/10.4213/tvp3381
  • http://mi.mathnet.ru/eng/tvp/v47/i1/p178

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bebbington M., Davydov Y., Zitikis R., “Estimating the renewal function when the second moment is infinite”, Stochastic Models, 23:1 (2007), 27–48  crossref  mathscinet  zmath  isi  elib  scopus
    2. Mitov K.V., Omey E., “Intuitive Approximations for the Renewal Function”, Stat. Probab. Lett., 84 (2014), 72–80  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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