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Article Dans Une Revue Annals of Probability Année : 2013

On strong approximation for the empirical process of stationary sequences

Résumé

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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Dates et versions

hal-00692546 , version 1 (30-04-2012)

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Jérôme Dedecker, Florence Merlevède, Emmanuel Rio. On strong approximation for the empirical process of stationary sequences. Annals of Probability, 2013, 41 (5), pp.3658-3696. ⟨10.1214/12-AOP798⟩. ⟨hal-00692546⟩
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