Distributional and local limit laws for a class of iterated maps that contract on average

Santos, Sara I and Walkden, Charles (2011) Distributional and local limit laws for a class of iterated maps that contract on average. [MIMS Preprint]

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Abstract

We consider iterated function schemes that contract on average with place-dependent probabilities. We are interested in generalisations of the central limit theorem, particularly to observations with infinite variance. By studying the spectral properties of an associated one-parameter family of transfer operators acting on an appropriate function space, we prove both a distributional and local limit law with convergence to a stable distribution.

Item Type: MIMS Preprint
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: 14 May 2011
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1620

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