Weak invariance principle and exponential bounds for some special functions of intermittent maps

Abstract

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