We study some generalizations of the LIL when self-normalizations are used. Two particular results proved are: (1) an extension of the Kolmogorov-Erdos test for partial sums of symmetric i.i.d. random variables having finite second moments; this result eliminates distinctions required when nonrandom normalizers are used and $E(X^2I(|X| > t))$ is not $O((L_2t)^{-1})$, and (2) an extension of a universal bounded LIL of Marcinkiewicz to nonsymmetric random variables. An interesting corollary of this work is a short new proof of the classical LIL avoiding truncation methods.
Publié le : 1991-01-14
Classification:
Law of the iterated logarithm,
Kolmogorov-Erdos test,
upper and lower functions,
self-normalizations,
60F15
@article{1176990551,
author = {Griffin, Philip and Kuelbs, James},
title = {Some Extensions of the LIL Via Self-Normalizations},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 380-395},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990551}
}
Griffin, Philip; Kuelbs, James. Some Extensions of the LIL Via Self-Normalizations. Ann. Probab., Tome 19 (1991) no. 4, pp. 380-395. http://gdmltest.u-ga.fr/item/1176990551/