Rates in the strong invariance principle for ergodic automorphisms of the torus - Archive ouverte HAL
Article Dans Une Revue Stochastics and Dynamics Année : 2014

Rates in the strong invariance principle for ergodic automorphisms of the torus

Résumé

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.
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Dates et versions

hal-00709413 , version 1 (19-06-2012)

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Jérôme Dedecker, Florence Merlevède, Françoise Pene. Rates in the strong invariance principle for ergodic automorphisms of the torus. Stochastics and Dynamics, 2014, 14 (2). ⟨hal-00709413⟩
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