Invariance principles for iterated maps that contract on average

Walkden, C.

doi:10.1090/S0002-9947-06-04322-4

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
DOI: https://doi.org/10.1090/S0002-9947-06-04322-4
Published electronically: October 17, 2006
MathSciNet review: 2262842
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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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