Treffer: SOME STRONG MIXING PROPERTIES OF A SEQUENCE OF RANDOM VARIABLES ARISING FROM α-CONTINUED FRACTIONS: Some strong mixing properties of a sequence of random variables arising from \(\alpha\)-continued fractions

Title:
SOME STRONG MIXING PROPERTIES OF A SEQUENCE OF RANDOM VARIABLES ARISING FROM α-CONTINUED FRACTIONS: Some strong mixing properties of a sequence of random variables arising from \(\alpha\)-continued fractions
Authors:
Rie Natsui, Hitoshi Nakada
Source:
Stochastics and Dynamics. :463-476
Publisher Information:
World Scientific Pub Co Pte Lt, 2003.
Publication Year:
2003
Subject Terms:
Metric theory of continued fractions, random variables, invariant measure, Stationary stochastic processes, mixing properties, Ergodicity, mixing, rates of mixing, Relations of ergodic theory with number theory and harmonic analysis, continued fractions, 0101 mathematics, 01 natural sciences
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1793-6799
0219-4937
DOI:
10.1142/s0219493703000802
Access URL:
https://www.worldscientific.com/doi/abs/10.1142/S0219493703000802
Accession Number:
edsair.doi.dedup.....e2f616edd0525fa986caedcf2c0caddc
Database:
OpenAIRE

Weitere Informationen

It is well known that the sequence of digits of regular continued fractions with the Gauss measure is ψ-mixing. In this paper we consider a class of semiregular continued fractions which are called α-continued fractions for α, 1/2≤α≤1. We show that the sequence of digits of α-continued fractions with the absolutely continuous invariant measure is absolutely regular for every α, 1/2≤α≤1, on the other hand, it is not φ-mixing for almost every α, 1/2≤α≤1.