Invariance principles for iterated maps that contract on average

Walkden, Charles (2007) Invariance principles for iterated maps that contract on average. Transactions of the American Mathematical Society, 359 (3). pp. 1081-1097. ISSN 0002-9947

PDF Invariance_Principles.pdf Restricted to Repository staff only Download (235kB)

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.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Ms Lucy van Russelt
Date Deposited:	03 Apr 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/763

Actions (login required)

View Item