A central limit theorem for time-dependent dynamical systems

Abstract

The work by Ott et al. (Math. Res. Lett. 16:463-475, ) 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 examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation technique in the form of Sethuraman and Varadhan (Electron. J. Probab. 10:121-1235, ). [ABSTRACT FROM AUTHOR]

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Description

Scholarly article / Open access (arXiv PDF)

Keywords

CENTRAL limit theorem, *DYNAMICS, *GAUSSIAN distribution, *MEMORY loss, *PERTURBATION theory, Central limit theorem, Limiting variance, Time-dependent systems

Citation

Nándori, P., Szász, D., & Varjú, T. (2012). A Central Limit Theorem for Time-Dependent Dynamical Systems. Journal of Statistical Physics, 146(6), 1213–1220. https://doi.org/10.1007/s10955-012-0451-8