Probability Surveys

Recent advances in invariance principles for stationary sequences

Florence Merlevède, Magda Peligrad, and Sergey Utev

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Abstract

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.

Article information

Source
Probab. Surveys Volume 3 (2006), 1-36.

Dates
First available: 13 January 2006

Permanent link to this document
http://projecteuclid.org/euclid.ps/1137162933

Digital Object Identifier
doi:10.1214/154957806100000202

Mathematical Reviews number (MathSciNet)
MR2206313

Zentralblatt MATH identifier
1189.60078

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 60F05: Central limit and other weak theorems

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

Citation

Merlevède, Florence; Peligrad, Magda; Utev, Sergey. Recent advances in invariance principles for stationary sequences. Probability Surveys 3 (2006), 1--36. doi:10.1214/154957806100000202. http://projecteuclid.org/euclid.ps/1137162933.


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