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Invariance principles for iterated maps that contract on average
Author(s):
C.
P.
Walkden
Journal:
Trans. Amer. Math. Soc.
359
(2007),
1081-1097.
MSC (2000):
Primary 60F17;
Secondary 37H99, 37A50
Posted:
October 17, 2006
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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:
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
Posted:
October 17, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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