On strong approximation for the empirical process of stationary sequences

Abstract : 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.
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Annals of Probability, Institute of Mathematical Statistics, 2013, 41 (5), pp.3658-3696
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Jérôme Dedecker, Florence Merlevède, Emmanuel Rio. On strong approximation for the empirical process of stationary sequences. Annals of Probability, Institute of Mathematical Statistics, 2013, 41 (5), pp.3658-3696. <hal-00692546>

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