Functional correlation decay and multivariate normal approximation for non-uniformly expanding maps

Abstract

In the setting of intermittent Pomeau–Manneville maps with time dependent parameters, we show a functional correlation bound widely useful for the analysis of the statistical properties of the model. We give two applications of this result, by showing that in a suitable range of parameters the bound implies the conditions of the normal approximation methods of Stein and Rio. For a single Pomeau–Manneville map belonging to this parameter range, both methods then yield a multivariate central limit theorem with a rate of convergence.