Some unbounded functions of intermittent maps for which the central limit theorem holds

Abstract

We compute some dependence coefficients for the stationary Markov chain whose transition kernel is the Perron-Frobenius operator of an expanding map $T$ of $[0,1]$ with a neutral fixed point. We use these coefficients to prove a central limit theorem for the partial sums of $f\circ T^i$, when $f$ belongs to a large class of unbounded functions from $[0,1]$ to $\mathbb{R}$. We also prove other limit theorems and moment inequalities.

16 pages