A Renewal Theorem of Blackwell Type
Embrechts, Paul ; Maejima, Makoto ; Omey, Edward
Ann. Probab., Tome 12 (1984) no. 4, p. 561-570 / Harvested from Project Euclid
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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.
Publié le : 1984-05-14
Classification:  Generalized renewal measures,  renewal theory,  regular variation,  Blackwell theorem,  60K05 
@article{1176993305,
     author = {Embrechts, Paul and Maejima, Makoto and Omey, Edward},
     title = {A Renewal Theorem of Blackwell Type},
     journal = {Ann. Probab.},
     volume = {12},
     number = {4},
     year = {1984},
     pages = { 561-570},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993305}
}

Embrechts, Paul; Maejima, Makoto; Omey, Edward. A Renewal Theorem of Blackwell Type. Ann. Probab., Tome 12 (1984) no. 4, pp.  561-570. http://gdmltest.u-ga.fr/item/1176993305/