Second order renewal theorem in the finite-means case
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 178-182
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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.
@article{TVP_2002_47_1_a15,
author = {A. Baltr\={u}nas and E. Omey},
title = {Second order renewal theorem in the finite-means case},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {178--182},
publisher = {mathdoc},
volume = {47},
number = {1},
year = {2002},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a15/}
}
A. Baltrūnas; E. Omey. Second order renewal theorem in the finite-means case. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 178-182. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a15/