Journal of Statistical Physics

, Volume 146, Issue 6, pp 1213–1220

A Central Limit Theorem for Time-Dependent Dynamical Systems

Authors

    • Institute of MathematicsBudapest University of Technology and Economics
  • Domokos Szász
    • Institute of MathematicsBudapest University of Technology and Economics
  • Tamás Varjú
    • Institute of MathematicsBudapest University of Technology and Economics
Article

DOI: 10.1007/s10955-012-0451-8

Cite this article as:
Nándori, P., Szász, D. & Varjú, T. J Stat Phys (2012) 146: 1213. doi:10.1007/s10955-012-0451-8

Abstract

The work by Ott et al. (Math. Res. Lett. 16:463–475, 2009) 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, 2005).

Keywords

Central limit theoremLimiting varianceTime-dependent systems

Copyright information

© Springer Science+Business Media, LLC 2012