A new weak dependence condition and applications to moment inequalities

The purpose of this paper is to propose a unifying weak dependence conditio n. Mixing sequences, functions of associated or Gaussian sequences, Bernoul li shifts as well as models with a Markovian representation are examples of the models considered. We establish Marcinkiewicz-Zygmund, Rosenthal and e xponential inequalities for general sequences of centered random variables. Inequalities are stated in terms of the decay rate for the covariance of p roducts of the initial random variables subject to the condition that the g ap of time between both products tends to infinity. As applications of thos e notions, we obtain a version of the functional CLT and an invariance prin ciple for the empirical process (C) 1999 Elsevier Science B.V. All rights r eserved. MSG: 60E15; 60F05; 60F17; 60G10; 60G99.