Doukhan, P.; Louhichi, S. A new weak dependence condition and applications to moment inequalities. (English) Zbl 0996.60020 Stochastic Processes Appl. 84, No. 2, 313-342 (1999). A new weak dependence condition for random sequences is proposed which is formulated in terms of covariances between past and future observations. It is proved that the new definition includes mixing sequences, functions of associated and Gaussian sequences as well as Bernoulli shifts and models with Markovian representation. A version of functional central limit theorem under the considered type of dependence is proved and an invariance principle for empirical processes is established. Reviewer: Zuzana Prášková (Praha) Cited in 30 ReviewsCited in 177 Documents MSC: 60E15 Inequalities; stochastic orderings 60F17 Functional limit theorems; invariance principles 60G10 Stationary stochastic processes 60F05 Central limit and other weak theorems Keywords:stationary sequences; weak dependence; mixing sequences; association; Rosenthal inequality; Marcinkiewicz-Zygmund inequality PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{S. Louhichi}, Stochastic Processes Appl. 84, No. 2, 313--342 (1999; Zbl 0996.60020) Full Text: DOI References: [1] Bahtin, Y., Bulinski, A.V., 1997. Fund. Appl. Math. 3, 1101-1108. (in Russian).; Bahtin, Y., Bulinski, A.V., 1997. Fund. Appl. Math. 3, 1101-1108. (in Russian). [2] Billingsley, P., 1968. Probability and Measure. Wiley, New York.; Billingsley, P., 1968. Probability and Measure. Wiley, New York. · Zbl 0172.21201 [3] Birkel, T., Moment bounds for associated sequences, Ann. 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