English

A new maximal inequality and invariance principle for stationary sequences

Probability 2007-05-23 v2

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.

Keywords

Cite

@article{arxiv.math/0406606,
  title  = {A new maximal inequality and invariance principle for stationary sequences},
  author = {Magda Peligrad and Sergey Utev},
  journal= {arXiv preprint arXiv:math/0406606},
  year   = {2007}
}

Comments

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