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:
https://doi.org/10.1090/S0002-9947-06-04322-4

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.