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April 1998 Darling-Erdős theorems for normalized sums of i.i.d. variables close to a stable law
Jean Bertoin
Ann. Probab. 26(2): 832-852 (April 1998). DOI: 10.1214/aop/1022855652

Abstract

Let $\xi, \xi_1, \dots$ be i.i.d. real-valued random variables and $S_n = \xi_1 + \dots + \xi_n$. In the case when the distribution of $\xi$ is close to a stable $(\alpha)$ law for some $\alpha \epsilon (0, 1) \bigcup (1, 2)$, we investigate the asymptotic behavior in distribution of the maximum of normalized sums, $\max_{k=1,\dots,n} k^{-1/\alpha}S_k$. This completes the Darling-Erdös limit theorem for the case $\alpha = 2$.

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Jean Bertoin. "Darling-Erdős theorems for normalized sums of i.i.d. variables close to a stable law." Ann. Probab. 26 (2) 832 - 852, April 1998. https://doi.org/10.1214/aop/1022855652

Information

Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0943.60041
MathSciNet: MR1626527
Digital Object Identifier: 10.1214/aop/1022855652

Subjects:
Primary: 60J30
Secondary: 60F05, 60G10

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 1998
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