Inégalités de mélange fort utilisant des normes d’Orlicz. (Strong mixing moment inequalities using Orlicz norms). (French) Zbl 0659.60009

We first extend the Orlicz inequality for covariances given by the first author [On strong mixing conditions for random fields and central limit theorem, Sov. Math., Dokl. (to appear)] to the Hilbert valued case. After this we show generalizations of the Marcinkiewicz-Zygmund inequality of higher order moments for sums of strongly mixing random variables extending to Orlicz case results by the second author and F. Portal [ibid. 297, Sér. I, 129-132 (1983; Zbl 0544.62022)] and the second author, J. Léon and F. Portal [ibid. 298, Sér. I, 305-308 (1984; Zbl 0557.60006)]. Orlicz norms allow weakening of moment assumptions. Interest of the results is explicited by the example of kernel density estimates.


60B05 Probability measures on topological spaces
60E15 Inequalities; stochastic orderings