Niemiro and Zieliński (2007) have recently obtained uniform asymptotic normality for the Bernoulli scheme. This paper concerns a similar problem. We show the uniform central limit theorem for a sequence of stationary random variables.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-2-1,
author = {Konrad Furma\'nczyk},
title = {A uniform central limit theorem for dependent variables},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {129-138},
zbl = {1168.60304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-2-1}
}
Konrad Furmańczyk. A uniform central limit theorem for dependent variables. Applicationes Mathematicae, Tome 36 (2009) pp. 129-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-2-1/