The Annals of Probability

A new maximal inequality and invariance principle for stationary sequences

Magda Peligrad and Sergey Utev

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Abstract

We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe [Ann. Probab. 28 (2000) 713–724]. Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed.

Article information

Source
Ann. Probab. Volume 33, Number 2 (2005), 798-815.

Dates
First available in Project Euclid: 3 March 2005

Permanent link to this document
http://projecteuclid.org/euclid.aop/1109868600

Digital Object Identifier
doi:10.1214/009117904000001035

Mathematical Reviews number (MathSciNet)
MR2123210

Zentralblatt MATH identifier
02164482

Subjects
Primary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles

Keywords
Asymptotic normality ergodic theorem functional central limit theorem invariance principle martingale maximal inequality Markov chains renewal sequences

Citation

Peligrad, Magda; Utev, Sergey. A new maximal inequality and invariance principle for stationary sequences. Ann. Probab. 33 (2005), no. 2, 798--815. doi:10.1214/009117904000001035. http://projecteuclid.org/euclid.aop/1109868600.


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