A new maximal inequality and invariance principle for stationary sequences
Peligrad, Magda ; Utev, Sergey
Ann. Probab., Tome 33 (2005) no. 1, p. 798-815 / Harvested from Project Euclid
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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.
Publié le : 2005-03-14
Classification:  Asymptotic normality,  ergodic theorem,  functional central limit theorem,  invariance principle,  martingale,  maximal inequality,  Markov chains,  renewal sequences,  60F05,  60F17 
@article{1109868600,
     author = {Peligrad, Magda and Utev, Sergey},
     title = {A new maximal inequality and invariance principle for stationary sequences},
     journal = {Ann. Probab.},
     volume = {33},
     number = {1},
     year = {2005},
     pages = { 798-815},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1109868600}
}

Peligrad, Magda; Utev, Sergey. A new maximal inequality and invariance principle for stationary sequences. Ann. Probab., Tome 33 (2005) no. 1, pp.  798-815. http://gdmltest.u-ga.fr/item/1109868600/