An invariance principle for maps with polynomial decay of correlations

Abstract

We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the iterates of discrete time maps display a polynomial decay of correlations.

15 pages

Cited by in corpus (8)

• Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
• Multiscale systems, homogenization, and rough paths
• Statistical properties of one-dimensional maps under weak hyperbolicity assumptions
• Rate of Convergence in the Weak Invariance Principle for Deterministic Systems
• Nice inducing schemes and the thermodynamics of rational maps
• Martingale-coboundary decomposition for families of dynamical systems
• Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
• Central Limit Theorems for Non-Invertible Measure Preserving Maps