Multifractal analysis on the level sets described by moving averages-Reference-Cited by-同舟云学术

Multifractal analysis on the level sets described by moving averages

Published:2015-10-21 Issue:07 Volume:11 Page:2175-2189
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Chen Haibo¹,Wang Xiaohua²,Wen Zhixiong³

Affiliation:

1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei 430073, P. R. China

2. China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, P. R. China

3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

Abstract

In this paper, the Hausdorff dimensions of level sets described by two kinds of moving averages are determined. The dissimilar results complement the work of Pfaffelhuber [Moving shift averages for ergodic transformation, Metrika22 (1975) 97–101] and del Junco and Steele [Moving averages of ergodic processes, Metrika24 (1977) 35–43], and reveal simultaneously that the two moving averages are of different convergence processes in the ergodic theory.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042115500967

Reference21 articles.

1. Distribution of frequencies of digits via multifractal analysis

2. Invertible measure preserving transformations and pointwise convergence

3. Convergence for moving averages

4. On the sum of digits of real numbers represented in the dyadic system.

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