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A central limit theorem for iterated random functions

Part of: Classical measure theory Limit theorems

Published online by Cambridge University Press:  14 July 2016

Wei Biao Wu  and
Michael Woodroofe
Wei Biao Wu*
Affiliation:
University of Michigan
Michael Woodroofe*
Affiliation:
University of Michigan
*
∗Postal address: Department of Statistics, The University of Michigan, 4062 Frieze Building, 105 South State St, Ann Arbor, MI 48109-1285, USA
∗Postal address: Department of Statistics, The University of Michigan, 4062 Frieze Building, 105 South State St, Ann Arbor, MI 48109-1285, USA
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Abstract

A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.

Keywords

Lipschitz continuityfractalsindicator functionsMarkov chainsPoisson's equationtransition operator

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 28A80: Fractals
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 748 - 755
Copyright
Copyright © Applied Probability Trust 2000 

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References

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