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A new maximal inequality and invariance principle for stationary sequences

Magda Peligrad·Sergey Utev
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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. 2005-04-12. A new maximal inequality and invariance principle for stationary sequences. https://doi.org/10.1214/009117904000001035

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