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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Invariance principles for iterated maps that contract on average


Author: C. P. Walkden
Journal: Trans. Amer. Math. Soc. 359 (2007), 1081-1097
MSC (2000): Primary 60F17; Secondary 37H99, 37A50
Published electronically: October 17, 2006
MathSciNet review: 2262842
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider iterated function schemes that contract on average. Using a transfer operator approach, we prove a version of the almost sure invariance principle. This allows the system to be modelled by a Brownian motion, up to some error term. It follows that many classical statistical properties hold for such systems, such as the weak invariance principle and the law of the iterated logarithm.


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Additional Information

C. P. Walkden
Affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
Email: cwalkden@maths.man.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04322-4
PII: S 0002-9947(06)04322-4
Received by editor(s): March 19, 2003
Received by editor(s) in revised form: November 25, 2004
Published electronically: October 17, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.