New techniques for empirical processes of dependent data

We present a new technique for proving the empirical process invariance principle for stationary processes (Xn)n≥0(Xn)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(Xn))n≥0(f(Xn))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.