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Statistical properties of endomorphisms and compact group extensions

Melbourne, Ian and Nicol, Matthew (2004) Statistical properties of endomorphisms and compact group extensions Journal of the London Mathematical Society.

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Abstract

The statistical properties of endomorphisms under the assumption that the associated Perron–Frobenius operator is quasicompact are considered. In particular, the central limit theorem, weak invariance principle and law of the iterated logarithm for sufficiently regular observations are examined. The approach clarifies the role of the usual assumptions of ergodicity, weak mixing, and exactness.

Sufficient conditions are given for quasicompactness of the Perron–Frobenius operator to lift to the corresponding equivariant operator on a compact group extension of the base. This leads to statistical limit theorems for equivariant observations on compact group extensions.

Examples considered include compact group extensions of piecewise uniformly expanding maps (for example Lasota–Yorke maps), and subshifts of finite type, as well as systems that are nonuniformly expanding or nonuniformly hyperbolic.

Item Type: Article
Additional Information: Published in the Journal of the London Mathematical Society (2004), 70:427-446. Cambridge University Press. Copyright © 2004 The london Mathematical Society. Reprinted with permission. Click here to visit the journal website.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1471

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