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VOL. 5 | 2009 Weak invariance principle and exponential bounds for some special functions of intermittent maps
Jérôme Dedecker, Florence Merlevède

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad

Abstract

We consider a parametric class Tγ of expanding maps of [0, 1] with a neutral fixed point at 0 for which there exists an unique invariant absolutely continuous probability measure νγ on [0, 1]. On the probability space ([0, 1], νγ), we prove the weak invariance principle for the partial sums of fTγi in some special cases involving non-standard normalization. We also prove new moment inequalities and exponential bounds for the partial sums of fTγi when f is some Hölder function such that f(0)=νγ(f).

Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.37008

Digital Object Identifier: 10.1214/09-IMSCOLL505

Subjects:
Primary: 37C30 , 37E05 , 60F17

Keywords: Exponential inequalities , Intermittency , Weak invariance principle

Rights: Copyright © 2009, Institute of Mathematical Statistics

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