Strong approximation results for the empirical process of stationary sequences

• Autores: Jérôme Dedecker, Florence Merlevède, Emmanuel Rio
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 5, 2013, págs. 3658-3696
• Idioma: inglés
• DOI: 10.1214/12-AOP798
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• Resumen

  • We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n−1−δ for some positive δ. This shows that our conditions are in some sense optimal.