A new maximal inequality and invariance principle for stationary sequences

Details A new maximal inequality and invariance principle for stationary sequences A new maximal inequality and invariance principle for stationary sequences

2004-06-29

arxiv.org/abs/math/0406606v2

Annals of Probability 2005, Vol. 33, No. 2, 798-815

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000001035 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000001035

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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