Merlevède, Florence; Peligrad, Magda; Utev, Sergey Recent advances in invariance principles for stationary sequences. (English) Zbl 1189.60078 Probab. Surv. 3, 1-36 (2006). 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. Cited in 66 Documents 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 Keywords:Brownian motion; weakly dependent sequences; martingale differences; linear process; central limit theorem; invariance principle PDFBibTeX XMLCite \textit{F. Merlevède} et al., Probab. Surv. 3, 1--36 (2006; Zbl 1189.60078) Full Text: DOI arXiv EuDML