Lindeberg theorem for Gibbs-Markov dynamics

Manfred Heinz Denker, Samuel Senti, Xuan Zhang

Research output: Contribution to journalArticle

Abstract

A dynamical array consists of a family of functions {fn,i1 : 1 ≤ i ≤ kn, n ≥ 1} and a family of initial times {τn,i : 1 ≤ i ≤ kn, n ≥ 1}. For a dynamical system (X, T) we identify distributional limits for sums of the form Sn = 1/sn kni=1 [fn,i TTn,i - an,i] n ≥ 1 for suitable (non-random) constants sn > 0 and an,i ϵ ℝ. We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from GibbsMarkov systems. Our results, which hold for more general dynamics, are stated in the context of GibbsMarkov dynamical systems for convenience.

Original languageEnglish (US)
Pages (from-to)4587-4613
Number of pages27
JournalNonlinearity
Volume30
Issue number12
DOIs
StatePublished - Nov 16 2017

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Central limit theorem
theorems
Dynamical systems
Dynamical system
Theorem
dynamical systems
Lipschitz
Time series
Family
Context
Form

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Denker, M. H., Senti, S., & Zhang, X. (2017). Lindeberg theorem for Gibbs-Markov dynamics. Nonlinearity, 30(12), 4587-4613. https://doi.org/10.1088/1361-6544/aa8ca2
Denker, Manfred Heinz ; Senti, Samuel ; Zhang, Xuan. / Lindeberg theorem for Gibbs-Markov dynamics. In: Nonlinearity. 2017 ; Vol. 30, No. 12. pp. 4587-4613.
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Denker, MH, Senti, S & Zhang, X 2017, 'Lindeberg theorem for Gibbs-Markov dynamics', Nonlinearity, vol. 30, no. 12, pp. 4587-4613. https://doi.org/10.1088/1361-6544/aa8ca2

Lindeberg theorem for Gibbs-Markov dynamics. / Denker, Manfred Heinz; Senti, Samuel; Zhang, Xuan.

In: Nonlinearity, Vol. 30, No. 12, 16.11.2017, p. 4587-4613.

Research output: Contribution to journalArticle

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