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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.
Received: 17.12.1999
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
Linking options:
https://www.mathnet.ru/eng/tvp3381https://doi.org/10.4213/tvp3381 https://www.mathnet.ru/eng/tvp/v47/i1/p178
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