Dedecker, Jérôme et al., Strong approximation results for the empirical process of stationary sequences, Annals of probability , 41(5), 2013, pp. 3658-3696
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n.1.. for some positive .. This shows that our conditions are in some sense optimal.