The Annals of Probability

Almost sure invariance principle for dynamical systems by spectral methods

Sébastien Gouëzel

Full-text: Open access

Abstract

We prove the almost sure invariance principle for stationary ℝd-valued random processes (with very precise dimension-independent error terms), solely under a strong assumption concerning the characteristic functions of these processes. This assumption is easy to check for large classes of dynamical systems or Markov chains using strong or weak spectral perturbation arguments.

Article information

Source
Ann. Probab., Volume 38, Number 4 (2010), 1639-1671.

Dates
First available in Project Euclid: 8 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1278593963

Digital Object Identifier
doi:10.1214/10-AOP525

Mathematical Reviews number (MathSciNet)
MR2663640

Zentralblatt MATH identifier
1207.60026

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems

Keywords
Almost sure invariance principle coupling transfer operator

Citation

Gouëzel, Sébastien. Almost sure invariance principle for dynamical systems by spectral methods. Ann. Probab. 38 (2010), no. 4, 1639--1671. doi:10.1214/10-AOP525. https://projecteuclid.org/euclid.aop/1278593963


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