A new maximal inequality and invariance principle for stationary sequences

A new maximal inequality and invariance principle for stationary sequences

Magda Peligrad and Sergey Utev

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

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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Primary Subjects: 60F05, 60F17

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

Full-text: Open access

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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

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