## 2007.59: Invariance principles for iterated maps that contract on average

2007.59:
Charles Walkden
(2007)
*Invariance principles for iterated maps that contract on average.*
Transactions of the American Mathematical Society, 359 (3).
pp. 1081-1097.
ISSN 0002-9947

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

## 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 |
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Subjects: | MSC 2000 > 37 Dynamical systems and ergodic theory MSC 2000 > 60 Probability theory and stochastic processes |

MIMS number: | 2007.59 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 03 April 2007 |

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