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.

21 pages; v.3: minor corrections according to comments by referee/pre-examiner

References in corpus (5)

• Rates of convergence in normal approximation under moment conditions via new bounds on solutions of the Stein equation
• Quasistatic dynamical systems
• Some unbounded functions of intermittent maps for which the central limit theorem holds
• An almost sure ergodic theorem for quasistatic dynamical systems
• Stein's method for dynamical systems

Cited by in corpus (6)

• Loss of memory and moment bounds for nonstationary intermittent dynamical systems
• Sunklodas' approach to normal approximation for time-dependent dynamical systems
• Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-mixing Nonuniformly Hyperbolic Maps
• A note on the finite-dimensional distributions of dispersing billiard processes
• Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps
• Central limit theorems with a rate of convergence for sequences of transformations