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The central limit theorem for $\sum f(\theta^nx)g(\theta^{n^2}x)$

Published online by Cambridge University Press:  10 November 2000

KATUSI FUKUYAMA
KATUSI FUKUYAMA
Affiliation:
Department of Mathematics, Kobe University, Rokko Kobe 657-8501, Japan
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Abstract

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In this paper, it is proved that the distribution of values of $N^{-1/2}\sum_{n=1}^N f_1(\theta^{p_1(n)}x)\dots f_K(\theta^{p_K(n)}x)$ converges to normal distribution. Here $p_k(n)$ are polynomials.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 5 , October 2000, pp. 1335 - 1353
Copyright
© 2000 Cambridge University Press