A central limit theorem for time-dependent dynamical systems

Abstract

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled Birkhoff-like partial sums of appropriate test functions. A substantial part of the problem is to ensure that the variances of the partial sums tend to infinity (cf. the zero-cohomology condition in the autonomous case). In fact, the present paper is the first one where non-random, i. e. specific examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation technique in the form of [9].

References in corpus (2)

• Non-stationary compositions of Anosov diffeomorphisms
• Central limit theorem for products of toral automorphisms

Cited by in corpus (13)

• A spectral approach for quenched limit theorems for random expanding dynamical systems
• Quasistatic dynamical systems
• Dispersing billiards with moving scatterers
• Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables
• Quasistatic dynamics with intermittency
• Central limit theorems for the shrinking target problem
• Quenched normal approximation for random sequences of transformations
• Central limit theorems with a rate of convergence for time-dependent intermittent maps
• Sunklodas' approach to normal approximation for time-dependent dynamical systems
• Almost sure invariance principle for sequential and non-stationary dynamical systems
• Central limit theorems with a rate of convergence for sequences of transformations
• Dynamical random walk on the integers with a drift
• Concentration inequalities for sequential dynamical systems of the unit interval