# Empirical processes of multidimensional systems with multiple mixing properties

@article{Dehling2010EmpiricalPO,
title={Empirical processes of multidimensional systems with multiple mixing properties},
author={Herold Dehling and Olivier Durieu},
journal={Stochastic Processes and their Applications},
year={2010},
volume={121},
pages={1076-1096}
}
• Published 7 April 2010
• Mathematics
• Stochastic Processes and their Applications
We establish a multivariate empirical process central limit theorem for stationary -valued stochastic processes (Xi)i>=1 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 etÂ al…
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