Second-order renewal theorem in the finite-means case
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,...
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| Veröffentlicht in: | Theory of probability and its applications 2003, Vol.47 (1), p.127-132 |
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| container_title | Theory of probability and its applications |
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| creator | BALTRUNAS, A OMEY, E |
| description | 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. |
| doi_str_mv | 10.1137/S0040585X97979561 |
| format | Article |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Exact sciences and technology Mathematics Probability and statistics Probability theory and stochastic processes Random variables Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) |
| title | Second-order renewal theorem in the finite-means case |
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