The large deviation estimate, used in classical proofs of the law of the iterated logarithm for i.i.d. random variables, implies the random variables satisfy a condition more stringent than a finite variance. Thus it is impossible to prove the law of the iterated logarithm in its full strength (i.e. assuming only a finite second moment) by using such a deviation estimate in a "straightforward" manner.
Publié le : 1973-06-14
Classification:
Large deviations,
law of the iterated logarithm,
Gaussian tail estimates,
60F10,
60F05,
60G50
@article{1176996946,
author = {Kostka, David G.},
title = {On Khintchine's Estimate for Large Deviations},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 509-512},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996946}
}
Kostka, David G. On Khintchine's Estimate for Large Deviations. Ann. Probab., Tome 1 (1973) no. 5, pp. 509-512. http://gdmltest.u-ga.fr/item/1176996946/