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Theoremes ergodiques perturbes

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Abstract

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.

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  1. Institut de Recherche Mathématique Avancée, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, F-67084, Strasbourg Cedex, France

    Dominique Schneider

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  1. Dominique Schneider
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Correspondence to Dominique Schneider.

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Schneider, D. Theoremes ergodiques perturbes. Isr. J. Math. 101, 157–178 (1997). https://doi.org/10.1007/BF02760927

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  • DOI: https://doi.org/10.1007/BF02760927

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