Empirical processes of Markov chains and dynamical systems indexed by classes of functions

Abstract

We study weak convergence of empirical processes of dependent data, indexed by classes of functions. We obtain results that are especially suitable for data arising from dynamical systems and Markov chains, where the Central Limit Theorem for partial sums is commonly derived via the spectral gap technique. Our results apply, e.g. to the empirical process of ergodic torus automorphisms.