HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-00630932
Contributor : Olivier Durieu Connect in order to contact the contributor
Submitted on : Tuesday, October 11, 2011 - 10:04:56 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:07 PM

Links full text

Identifiers

Collections

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⟩

Share

Metrics

Record views

146