The CLT for rotated ergodic sums and related processes

Guy Cohen, Jean Pierre Conze

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let (Ω,A, P,τ) be an ergodic dynamical system. The rotated ergodic sums of a function f on Ω for θ ∈ ℝ are S nθf:= Σk=0n-1 e 2πikθ foτk, n ≥ 1. Using Carleson's theorem on Fourier series, Peligrad and Wu proved in [14] that (S nθf)n≥1 satisfies the CLT for a.e. θ when (f oτn) is a regular process. Our aim is to extend this result and give a simple proof based on the Fejér-Lebesgue theorem. The results are expressed in the framework of processes generated by K-systems. We also consider the invariance principle for modified rotated sums. In a last section, we extend the method to ℤd-dynamical systems.

Original languageEnglish
Pages (from-to)3981-4002
Number of pages22
JournalDiscrete and Continuous Dynamical Systems
Volume33
Issue number9
DOIs
StatePublished - 1 Sep 2013

Keywords

  • Central limit theorem
  • K-systems
  • Rotated process

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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