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

2012/06/19 by Dedecker, Jérôme, Merlevède, Florence, Pene, Francoise
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1206.4336

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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