Rates in almost sure invariance principle for slowly mixing dynamical systems

Abstract : We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Manneville intermittent maps, with Hölder continuous observables. Our rates have form o(n γ L(n)), where L(n) is a slowly varying function and γ is determined by the speed of mixing. We strongly improve previous results where the best available rates did not exceed O(n 1/4). To break the O(n 1/4) barrier, we represent the dynamics as a Young-tower-like Markov chain and adapt the methods of Berkes-Liu-Wu and Cuny-Dedecker-Merlevède on the Komlós-Major-Tusnády approximation for dependent processes.
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Pré-publication, Document de travail
MAP5 2018-02. 2018
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Dernière modification le : jeudi 31 mai 2018 - 09:12:02
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  • HAL Id : hal-01688705, version 1

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C Cuny, J Dedecker, A Korepanov, Florence Merlevède. Rates in almost sure invariance principle for slowly mixing dynamical systems. MAP5 2018-02. 2018. 〈hal-01688705〉

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