We prove that the $\lim \inf$ of suitably normalized sums of i.i.d. nonnegative and nondegenerate random variables can with probability 1 only be a constant between $-2^{1/2}$ and 0. Moreover, we show that each value within this range is attainable by an appropriate choice of the underlying common distribution function.
Publié le : 1994-10-14
Classification:
Law of the iterated logarithm,
domain of attraction of a stable law or normal law,
quantile function,
60F15
@article{1176988485,
author = {Mason, David M.},
title = {A Universal One-Sided Law of the Iterated Logarithm},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1826-1837},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988485}
}
Mason, David M. A Universal One-Sided Law of the Iterated Logarithm. Ann. Probab., Tome 22 (1994) no. 4, pp. 1826-1837. http://gdmltest.u-ga.fr/item/1176988485/