Rates in almost sure invariance principle for slowly mixing dynamical systems - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2020

Rates in almost sure invariance principle for slowly mixing dynamical systems

Résumé

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.
Fichier principal
Vignette du fichier
KMT-LSV-revised-12-nov-2018.pdf (367.67 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01688705 , version 1 (19-01-2018)
hal-01688705 , version 2 (20-11-2018)

Identifiants

Citer

C Cuny, J Dedecker, A Korepanov, Florence Merlevède. Rates in almost sure invariance principle for slowly mixing dynamical systems. Ergodic Theory and Dynamical Systems, 2020, ⟨10.1017/etds.2019.2⟩. ⟨hal-01688705v2⟩
250 Consultations
373 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More