Empirical central limit theorems for ergodic automorphisms of the torus

الأصل · EN

Let T be an ergodic automorphism of the d-dimensional torus Tᵈ, and f be a continuous function from Tᵈ to Rˡ. On the probability space Tᵈ equipped with the Lebesgue-Haar measure, we prove the weak convergence of the sequential empirical process of the sequence (f o Tⁱ)ᵢ ≥ ₁ under some mild conditions 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 filtration.