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Recent advances in invariance principles for stationary sequences. (English) Zbl 1189.60078

Summary: In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance principles, and also they have interest in themselves. The classes of dependent random variables considered will be martingale-like sequences, mixing sequences, linear processes, additive functionals of ergodic Markov chains.

MSC:

60G10 Stationary stochastic processes
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
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