Doukhan, Paul; Wintenberger, Olivier An invariance principle for weakly dependent stationary general models. (English) Zbl 1124.60031 Probab. Math. Stat. 27, No. 1, 45-73 (2007). Summary: The aim of this paper is to refine a weak invariance principle for stationary sequences given by P. Doukhan and S. Louhichi [Stochastic Processes Appl. 84, No. 2, 313–342 (1999; Zbl 0996.60020)]. Since our conditions are not causal, our assumptions need to be stronger than the mixing and causal \(\theta\)-weak dependence assumptions used by J. Dedecker and P. Doukhan [Stochastic Processes Appl. 106, No. 1, 63–80 (2003; Zbl 1075.60513)]. Here, if moments of order greater than 2 exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan and Louhichi [loc. cit.] assumed the existence of moments with order greater than 4. Besides the \(\eta\)- and \(\kappa\)-weak dependence conditions used previously, we introduce a weaker one, \(\lambda\), which fits the Bernoulli shifts with dependent inputs. Cited in 1 ReviewCited in 22 Documents MSC: 60F17 Functional limit theorems; invariance principles Keywords:weak dependence; Bernoulli shifts Citations:Zbl 0996.60020; Zbl 1075.60513 PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{O. Wintenberger}, Probab. Math. Stat. 27, No. 1, 45--73 (2007; Zbl 1124.60031) Full Text: arXiv