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

Published 2012-05-31Version 1

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.