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 sequences in Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal θ-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharp result which improves on an optimal one in Doukhan et alii (1995) under strong mixing. We prove this result and we also precise convergence rates under existence of moments 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 some general classes of stationary and weakly dependent sequences. Besides the previously used ηand κ-weak dependence conditions, we introduce a mixed condition, λ, adapted to consider Bernoulli shifts with dependent inputs.