Teugels' Renewal Theorem and Stable Laws
Mohan, N. R.
Ann. Probab., Tome 4 (1976) no. 6, p. 863-868 / Harvested from Project Euclid
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Let $\{S_n\}, n = 1,2, \cdots$ denote the partial sums of a sequence of independent, identically distributed nonnegative random variables with common distribution function $F$ having finite mean $\mu$, and let $H(t) = \sum^\infty_{n=1} P(S_n \leqq t)$. Further, let $F$ be nonarithmetic. It is shown in this paper that as $t \rightarrow \infty H(t) - t/\mu$ is regularly varying if and only if $F$ belongs to the domain of attraction of a stable law with exponent $\alpha, 1 < \alpha \leqq 2$.
Publié le : 1976-10-14
Classification:  Renewal function,  nonarithmetic,  regular and slow variation,  domain of attraction,  stable law,  key renewal theorem,  relatively stable,  60K05 
@article{1176995991,
     author = {Mohan, N. R.},
     title = {Teugels' Renewal Theorem and Stable Laws},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 863-868},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995991}
}

Mohan, N. R. Teugels' Renewal Theorem and Stable Laws. Ann. Probab., Tome 4 (1976) no. 6, pp.  863-868. http://gdmltest.u-ga.fr/item/1176995991/