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July 1996 Large deviations and law of the iterated logarithm for partialsums normalized by the largest absolute observation
Lajos Horváth, Qi-Man Shao
Ann. Probab. 24(3): 1368-1387 (July 1996). DOI: 10.1214/aop/1065725185

Abstract

Let ${X_n, 1 \leq n < \infty}$ be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index $0 < \alpha < 2$. The limit of $x_n^{-1}\log P{S_n/ \max |X_i| \geq x_n}$ is found when $x_n \to \infty$ and $\x_n/n \to 0$. The large deviation result is used to prove the law of the iterated logarithm for the self-normalized partial sums.

Citation

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Lajos Horváth. Qi-Man Shao. "Large deviations and law of the iterated logarithm for partialsums normalized by the largest absolute observation." Ann. Probab. 24 (3) 1368 - 1387, July 1996. https://doi.org/10.1214/aop/1065725185

Information

Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0869.60025
MathSciNet: MR1411498
Digital Object Identifier: 10.1214/aop/1065725185

Subjects:
Primary: 60F10, 60F15
Secondary: 60G18, 60G50

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 3 • July 1996
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