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/