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
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by C. P. Walkden PDF

Trans. Amer. Math. Soc. 359 (2007), 1081-1097 Request permission

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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