If $X$ takes values in a Banach space $B$ and is in the domain of normal attraction of a Gaussian law on $B$ with $EX = 0, E(\|X\|^2/L_2\|X\|) < \infty$, then it is known that $X$ satisfies the compact law of the iterated logarithm as described in Goodman, Kuelbs and Zinn [9], Theorem 4.1. In this paper the analogous result is demonstrated when $X$ is merely in the domain of attraction of a Gaussian law. The functional LIL is also obtained in this setting. These results refine Corollary 7 of Kuelbs and Zinn [22], as well as various functional LILs.
Publié le : 1985-08-14
Classification:
Law of the iterated logarithm,
cluster set,
domain of attraction of a Gaussian random variable,
60B05,
60B11,
60B12,
60F10,
60F15,
28C20,
60B10
@article{1176992910,
author = {Kuelbs, J.},
title = {The LIL when $X$ is in the Domain of Attraction of a Gaussian Law},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 825-859},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992910}
}
Kuelbs, J. The LIL when $X$ is in the Domain of Attraction of a Gaussian Law. Ann. Probab., Tome 13 (1985) no. 4, pp. 825-859. http://gdmltest.u-ga.fr/item/1176992910/