AN EMPIRICAL FUNCTIONAL CENTRAL LIMIT THEOREM FOR
WEAKLY DEPENDENT SEQUENCES
Abstract: In this paper we obtain a Functional Central Limit Theorem for the empirical
process of a stationary sequence under a new weak dependence condition introduced by
Doukhan and Louhichi . This result improves on the Empirical Functional Central Limit
Theorem in Doukhan and Louhichi . Our proof relies on new moment inequalities and on a
Central Limit Theorem. Techniques of proofs come from Louhichi  and Rio ,
respectively. We also deduce a rate of convergence in a Marcinkiewicz-Zygmund Strong
2000 AMS Mathematics Subject Classification: 60E15, 60F05, 60F15, 60F17, 60G10.
Key words and phrases: Stationary sequences, Rosenthal inequality, moment
inequalities, Functional Central Limit Theorem, empirical process, Marcinkiewicz-Zygmund
Strong Law, weakly dependent sequences, Lindeberg Theorem.