Dedecker, Jérôme; Doukhan, Paul A new covariance inequality and applications. (English) Zbl 1075.60513 Stochastic Processes Appl. 106, No. 1, 63-80 (2003). Three measures of dependence, i.e.strong mixing-type, mixingale-type and s-weak dependence coefficients are considered and compared and useful examples describing the behaviour of these coefficients are given. Further, a new covariance inequality based on mixingale type coefficient is proved and compared with a similar result developed recently for strong mixing sequences. New sufficient conditions to obtain sharp versions of Donsker invariance principle and Marcinkiewicz strong law of large numbers for weakly dependent sequences are established. Reviewer: Zuzana Prášková (Praha) Cited in 2 ReviewsCited in 57 Documents MSC: 60F17 Functional limit theorems; invariance principles 60G10 Stationary stochastic processes 60G48 Generalizations of martingales Keywords:strong mixing; mixingales; s-weak dependence; weak invariance principle; strong laws of large numbers PDFBibTeX XMLCite \textit{J. Dedecker} and \textit{P. Doukhan}, Stochastic Processes Appl. 106, No. 1, 63--80 (2003; Zbl 1075.60513) Full Text: DOI References: [1] Ango Nzé, P., Critères d’ergodicité géométrique ou arithmétique de modèles linéaires perturbés à représentation markovienne, C. R. Acad. Sci. Paris Sér. 1, 326, 371-376 (1998) · Zbl 0918.60052 [2] Ango Nzé, P.; Bühlman, P.; Doukhan, P., Weak dependence beyond mixing and asymptotics for nonparametric regression, Ann. 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