Lindeberg theorem for Gibbs-Markov dynamics

Manfred Denker, Samuel Senti, Xuan Zhang

Research output: Contribution to journalArticle

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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

All Science Journal Classification (ASJC) codes

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

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    Denker, M., Senti, S., & Zhang, X. (2017). Lindeberg theorem for Gibbs-Markov dynamics. Nonlinearity, 30(12), 4587-4613. https://doi.org/10.1088/1361-6544/aa8ca2