The central limit theorem and ergodicity

Yingxuan Niu and Yi Wang

Statistics & Probability Letters, 2010, vol. 80, issue 15-16, 1180-1184

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.

Keywords: The; central; limit; theorem; Topologically; ergodic; Topologically; strongly; ergodic; E-system (search for similar items in EconPapers)
Date: 2010
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