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# Central limit theorem for some classes of dynamical systems

Rahman, Mohammad Mahbubur (1997) Central limit theorem for some classes of dynamical systems. Masters thesis, Concordia University.

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## Abstract

We consider a transformation T of the unit interval (0, 1) into itself which is piecewise $C\sp2$ and expanding. Using the spectral decomposition of the Frobenius-Perron operator of T, we give a proof of the Central Limit Theorem for$$\left({1\over n}\right)\sum\sbsp{i=0}{n-1}f\circ T\sp{i},$$where f is a function of bounded variation. It is also shown that the speed of covergence in the Central Limit Theorem is of the order ${1\over\sqrt n}.$

Divisions: Concordia University > Faculty of Arts and Science > Mathematics and Statistics Thesis (Masters) Rahman, Mohammad Mahbubur v, 71 leaves ; 29 cm. Concordia University M.Sc. Mathematics 1997 Gora, Pawel QA 273.67 R34 1997 236 Concordia University Library 27 Aug 2009 17:10 13 Jul 2020 19:46 https://concordiauniversity.on.worldcat....
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