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Abstract: We establish a multivariate empirical process central limit theorem for stationary -valued stochastic processes under very weak conditions concerning the dependence structure of the process. As an application, we can prove the empirical process CLT for ergodic torus automorphisms. Our results also apply to Markov chains and dynamical systems having a spectral gap on some Banach space of functions. Our proof uses a multivariate extension of the techniques introduced by Dehling et al. (2009) in the univariate case. As an important technical ingredient, we prove a th moment bound for partial sums in multiple mixing systems. [Copyright &y& Elsevier]

Abstract: We present a new technique for proving the empirical process invariance principle for stationary processes . 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 , 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. [Copyright &y& Elsevier]