A central limit theorem for time-dependent dynamical systems

Details A central limit theorem for time-dependent dynamical systems A central limit theorem for time-dependent dynamical systems

2011-10-31

arxiv.org/abs/1111.0027v1

Mathematics

Dynamical Systems

Scientific paper

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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