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 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 be the empirical repartition function of the sequence and its
repartition function. There is, moreover, given, for the multidimensional case, a
weak invariance principle. A stationary sequence of Gaussian processes such
that
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: -