CALCUL DE LA VITESSE DE CONVERGENCE DANS LE THEOIEME
CENTRAL LIMITE VIS A VIS DES DISTANCES DE PMOHOROV, DUDLEY
ET LEVY DANS LE CAS DE VARIABLES ALEATOIMES DEPENDANTES
P. Doukhan
J. Leon
F. Portal
Abstract: The paper gives a general framework to estimate Dudley and Lévy’s metrics for
Hilbert space valued random variables and Prohorov’s one for the -dimensional
distributions of an -valued process, in the case of central limit theorem for stationary and
mixing random variables. The speeds of convergence obtained here are approximately
and where is the length of the observed sample and with
quite strong mixing hypotheses.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -