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

International audienceIn 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 for which the partial sum of f o T +... + f o T^n satisfies a strong invariance principle with an explicit rate of convergence