Empirical central limit theorems for ergodic automorphisms of the torus

Abstract : Let T be an ergodic automorphism of the d-dimensional torus T^d , and f be a continuous function from T^d to R . On the probability space T^d equipped with the Lebesgue-Haar measure, we prove the weak convergence of the sequential empirical process of the sequence (f ° T^ i )i≥1 under some condition on the modulus of continuity of f . The proofs are based on new limit theorems and new inequalities for non-adapted sequences, and on new estimates of the conditional expectations of f with respect to a natural ltration.
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Jérôme Dedecker, Florence Merlevède, Françoise Pene. Empirical central limit theorems for ergodic automorphisms of the torus. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2013, 10 (2), pp.731-766. ⟨hal-00741466⟩

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