Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus

J. Dedecker; F. Merlevède; F. Pène

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arXiv · 1205.7022

Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus

J. Dedecker·F. Merlevède·F. Pène

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Abstract

In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus, even in the non hyperbolic case. In this context, we give a large class of unbounded functions f from the d-dimensional torus to R, for which the partial sum foT+ foT^2 + ... + foT^n satisfies a strong invariance principle with an explicit rate of convergence.

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BibTeX RIS

J. Dedecker, F. Merlevède, F. Pène. 2012-05-31. Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus. https://arxiv.org/abs/1205.7022

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