# An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Abstract : Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$, under which weak convergence of $(U_n(t))_{t\in\R^d}$ can be proved. This is particularly useful when dealing with data arising from dynamical systems or functional of Markov chains. This result improves those of [DDV09] and [DD11], where the technique was first introduced, and provides new applications.
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https://hal.archives-ouvertes.fr/hal-00630932
Contributor : Olivier Durieu <>
Submitted on : Tuesday, October 11, 2011 - 10:04:56 AM
Last modification on : Monday, February 18, 2019 - 5:12:07 PM

### Citation

Olivier Durieu, Marco Tusche. An Empirical Process Central Limit Theorem for Multidimensional Dependent Data. Journal of Theoretical Probability, Springer, 2014, 27 (1), pp.249-277. ⟨10.1007/s10959-012-0450-3⟩. ⟨hal-00630932⟩

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