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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 8, Fasc. ,
pages 117 - 132
 

PRINCIPE D’INVARIANCE FAIBLE POUR LA FONCTION DE REPARTITION EMPIRIQUE DANS UN CADRE MULTIDIMENSIONNEL ET MELANGEANT

Paul Doukhan
Frederic Portal

Abstract: A strictly stationary and strongly or uniformly mixing sequence of random variables (q ), n n > 0, is considered. There are given estimates of even moments for partial sums of Marcinkiewicz-Zygmund type and an exponential inequality for the case of a geometrically uniformly mixing random sequence.

Let F n be the empirical repartition function of the sequence (q ) n and F its repartition function. There is, moreover, given, for the multidimensional case, a weak invariance principle. A stationary sequence Y n of Gaussian processes such that

V~ -- -a -a ---1---- P(sRudp| n(Fn - F)- Yn|> bn ) < bn with a ~~ 3(5d + 4)
is constructed.

For the estimate of the Prohorov distance a calculus of oscillations and a multidimensional central limit theorem were applied.

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

Key words and phrases: -

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