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The central limit theorem and ergodicity

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  • Niu, Yingxuan
  • Wang, Yi

Abstract

In this work, some relationships between stochastic properties and topological properties of dynamical systems are investigated. Let f be a continuous map from a compact metric space X to itself. We prove that if f satisfies the central limit theorem, then f is topologically strongly ergodic and (X,f) is an E-system, that is, f is topologically transitive and there is an invariant Borel probability measure m with full support.

Suggested Citation

  • Niu, Yingxuan & Wang, Yi, 2010. "The central limit theorem and ergodicity," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1180-1184, August.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1180-1184
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    References listed on IDEAS

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    1. Gu, Rongbao, 2007. "The large deviations theorem and ergodicity," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1387-1392.
    2. Niu, Yingxuan, 2009. "The large deviations theorem and sensitivity," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 609-614.
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