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.
Document type :
Preprints, Working Papers, ...
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01688705
Contributor : Jérôme Dedecker <>
Submitted on : Tuesday, November 20, 2018 - 2:47:19 PM
Last modification on : Thursday, April 11, 2019 - 4:02:50 PM

File

KMT-LSV-revised-12-nov-2018.pd...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01688705, version 2

Collections

Citation

C Cuny, J Dedecker, A Korepanov, Florence Merlevède. Rates in almost sure invariance principle for slowly mixing dynamical systems. 2018. ⟨hal-01688705v2⟩

Share

Metrics

Record views

80

Files downloads

94