A central limit theorem for time-dependent dynamical systems

2011/10/31 by Peter Nandori, Domokos Szasz, Tamas Varju · 1 citation
Mathematics · #math.DS #msc:37A50 #msc:60F05

paper · pdf · doi:10.1007/s10955-012-0451-8

published as Journal of Statistical Physics, 146, 6: 1213-1220, 2012

arxiv created 2011/10/31 · arxiv updated 2016/03/25

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].

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