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.
Publié le : 1996-07-14
Classification:
Stable law,
domain of attraction,
large deviation,
law of the iterated logarithm,
self-normalized partial sums,
largest absolute observation,
60F10,
60F15,
60G50,
60G18
@article{1065725185,
author = {Horv\'ath, Lajos and Shao, Qi-Man},
title = {Large deviations and law of the iterated logarithm for partial
sums normalized by the largest absolute observation},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1368-1387},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725185}
}
Horváth, Lajos; Shao, Qi-Man. Large deviations and law of the iterated logarithm for partial
sums normalized by the largest absolute observation. Ann. Probab., Tome 24 (1996) no. 2, pp. 1368-1387. http://gdmltest.u-ga.fr/item/1065725185/