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A new weak dependence condition and applications to moment inequalities. (English) Zbl 0996.60020
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.

MSC:
60E15 Inequalities; stochastic orderings
60F17 Functional limit theorems; invariance principles
60G10 Stationary stochastic processes
60F05 Central limit and other weak theorems
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