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.
Citation
Magda Peligrad. Sergey Utev. "A new maximal inequality and invariance principle for stationary sequences." Ann. Probab. 33 (2) 798 - 815, March 2005. https://doi.org/10.1214/009117904000001035
Information