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2006 Recent advances in invariance principles for stationary sequences
Florence Merlevède, Magda Peligrad, Sergey Utev
Probab. Surveys 3: 1-36 (2006). DOI: 10.1214/154957806100000202


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.


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Florence Merlevède. Magda Peligrad. Sergey Utev. "Recent advances in invariance principles for stationary sequences." Probab. Surveys 3 1 - 36, 2006.


Published: 2006
First available in Project Euclid: 13 January 2006

zbMATH: 1189.60078
MathSciNet: MR2206313
Digital Object Identifier: 10.1214/154957806100000202

Primary: 60F05 , 60G51

Keywords: Brownian motion , central limit theorem , invariance principle , linear process , martingale differences , weakly dependent sequences

Rights: Copyright © 2006 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.3 • 2006
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