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Iterates of expanding maps


Barbour, A D; Gerrard, R; Reinert, G (2000). Iterates of expanding maps. Probability Theory and Related Fields, 116(2):151-180.

Abstract

The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random. In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling and Stein's method.

The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random. In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling and Stein's method.

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12 citations in Web of Science®
11 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Expanding maps – Functional iteration – Coupling – Decay of correlations – Gaussian approximation
Language:English
Date:2000
Deposited On:07 Apr 2010 13:02
Last Modified:05 Apr 2016 13:25
Publisher:Springer
ISSN:0178-8051
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:10.1007/PL00008725
Permanent URL: http://doi.org/10.5167/uzh-22063

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