Theoremes ergodiques perturbes

We obtain results on almost sure convergence of ergodic averages along arithmetic subsequences perturbed by independent identically distributed random variables having ap ^th finite moment for somep>0. To prove these results, we use methods based on the harmonic analysis and the theory of Gaussian processes. In fact that will express the stability of Bourgain’s results concerning convergence of ergodic averages for certain arithmetic subsequences.