Open Access
May, 1984 A Renewal Theorem of Blackwell Type
Paul Embrechts, Makoto Maejima, Edward Omey
Ann. Probab. 12(2): 561-570 (May, 1984). DOI: 10.1214/aop/1176993305


Suppose $\{X_1, X_2, \cdots\}$ are i.i.d. random variables with finite mean $0 < E(X_1) < \infty$. If $S_n$ stands for the $n$th partial sum, and $\{a(n)\}_n$ is a sequence of nonnegative numbers, then $G(x) = \sum^\infty_{n = 0} a(n)P\{S_n \leq x\}$ is a generalized renewal measure. We investigate the behaviour of $G(x + h) - G(x)$ as $x \rightarrow \infty$ for $\{a(n)\}_n$ regularly varying.


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Paul Embrechts. Makoto Maejima. Edward Omey. "A Renewal Theorem of Blackwell Type." Ann. Probab. 12 (2) 561 - 570, May, 1984.


Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0537.60087
MathSciNet: MR735853
Digital Object Identifier: 10.1214/aop/1176993305

Primary: 60K05

Keywords: Blackwell theorem , Generalized renewal measures , regular variation , renewal theory

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 2 • May, 1984
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