New techniques for empirical processes of dependent data

We present a new technique for proving the empirical process invariance principle for stationary processes ( X n ) n ≥ 0 . The main novelty of our approach lies in the fact that we only require the central limit theorem and a moment bound for a restricted class of functions ( f ( X n ) ) n ≥ 0 , not containing the indicator functions. Our approach can be applied to Markov chains and dynamical systems, using spectral properties of the transfer operator. Our proof consists of a novel application of chaining techniques.