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 f○Tγi in some special cases involving non-standard normalization. We also prove new moment inequalities and exponential bounds for the partial sums of f○Tγi when f is some Hölder function such that f(0)=νγ(f).
Information
Digital Object Identifier: 10.1214/09-IMSCOLL505