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Contents of PMS, Vol. 6, Fasc. 1,
pages 19 - 27
 

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 k -dimensional distributions of an Rd -valued process, in the case of central limit theorem for stationary and mixing random variables. The speeds of convergence obtained here are approximately n- 1/4, n-1/12 and k5/8n -1/12, where n is the length of the observed sample and with quite strong mixing hypotheses.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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