An Invariance Principle for New Weakly Dependent Stationary Models using Sharp Moment Assumptions

This paper is aimed at sharpen a weak invariance principle for stationary sequencesin Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharpresult which improves on an optimal one in Doukhan et alii (1995) under strongmixing. We prove this result and we also precise convergence rates under existence ofmoments with order > 2 while Doukhan & Louhichi (1999) assume a moment of order> 4. Analogously to those authors, we use a non-causal condition to deal with somegeneral classes of stationary and weakly dependent sequences. Besides the previouslyused - and -weak dependence conditions, we introduce a mixed condition, , adaptedto consider Bernoulli shifts with dependent inputs.