Abstract : Let T be an ergodic automorphism of the d-dimensional torus. In the spirit of Le Borgne, we give conditions on the Fourier coeffi cients of a real valued function f under which the Birkhoff sums satis fy a strong invariance principle. Next, reinforcing the condition on the Fourier coeffi cients in a natural way, we obtain explicit rates of convergence in the strong invariance principle.
https://hal.archives-ouvertes.fr/hal-00709413
Contributeur : Francoise Pene
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Soumis le : mardi 19 juin 2012 - 21:25:13
Dernière modification le : jeudi 31 mai 2018 - 09:12:01
Document(s) archivé(s) le : jeudi 20 septembre 2012 - 02:21:17
Jérôme Dedecker, Florence Merlevède, Françoise Pene. Rates in the strong invariance principle for ergodic automorphisms of the torus. Stochastics and Dynamics, World Scientific Publishing, 2014, 14 (2). 〈hal-00709413〉
