On the functional central limit theorem for stationary processes

We give a sufficient condition for a stationary sequence of square-integrab le and real-valued random variables to satisfy a Donsker-type invariance pr inciple. This condition is similar to the L-1-criterion of Gordin for the u sual central limit theorem and provides invariance principles for alpha-mix ing or beta-mixing sequences as well as stationary Markov chains. In the la tter case, we present an example of a non irreducible and non cc-mixing cha in to which our result applies. (C) 2000 Editions scientifiques et medicale s Elsevier SAS.