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arXiv · 1206.4336

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

Jérôme Dedecker·Florence Merlevède·Francoise Pene
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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.

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Jérôme Dedecker, Florence Merlevède, Francoise Pene. 2012-06-19. Rates in the strong invariance principle for ergodic automorphisms of the torus. https://arxiv.org/abs/1206.4336

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