Hostname: page-component-7dd5485656-7jgsp Total loading time: 0 Render date: 2025-10-30T19:25:44.897Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable