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March 2005 A new maximal inequality and invariance principle for stationary sequences
Magda Peligrad, Sergey Utev
Ann. Probab. 33(2): 798-815 (March 2005). DOI: 10.1214/009117904000001035

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.

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Magda Peligrad. Sergey Utev. "A new maximal inequality and invariance principle for stationary sequences." Ann. Probab. 33 (2) 798 - 815, March 2005. https://doi.org/10.1214/009117904000001035

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1070.60025
MathSciNet: MR2123210
Digital Object Identifier: 10.1214/009117904000001035

Subjects:
Primary: 60F05 , 60F17

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

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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