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The central limit theorem and ergodicity

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.
Year of publication:
2010
Authors: Niu, Yingxuan ; Wang, Yi
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 80.2010, 15-16, p. 1180-1184
Publisher: Elsevier
Keywords: The central limit theorem Topologically ergodic Topologically strongly ergodic E-system
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008488236
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