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October, 1976 Teugels' Renewal Theorem and Stable Laws
N. R. Mohan
Ann. Probab. 4(5): 863-868 (October, 1976). DOI: 10.1214/aop/1176995991

Abstract

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 $\alpha, 1 < \alpha \leqq 2$.

Citation

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N. R. Mohan. "Teugels' Renewal Theorem and Stable Laws." Ann. Probab. 4 (5) 863 - 868, October, 1976. https://doi.org/10.1214/aop/1176995991

Information

Published: October, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0352.60062
MathSciNet: MR418271
Digital Object Identifier: 10.1214/aop/1176995991

Subjects:
Primary: 60K05

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 5 • October, 1976
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