Strong laws of large numbers, obtained for positive, independent random variables, are utilized to prove iterated logarithm laws (with a nonrandom normalizing sequence) for a class of martingales. A law of the iterated logarithm is also established for certain random quadratic forms.
Publié le : 1980-08-14
Classification:
Strong law of large numbers,
stability,
law of the iterated logarithm,
$U$-statistics,
random quadratic forms,
60F15
@article{1176994664,
author = {Fernholz, Luisa Turrin and Teicher, Henry},
title = {Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 765-774},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994664}
}
Fernholz, Luisa Turrin; Teicher, Henry. Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms. Ann. Probab., Tome 8 (1980) no. 6, pp. 765-774. http://gdmltest.u-ga.fr/item/1176994664/