SOME STRONG MIXING PROPERTIES OF A SEQUENCE OF RANDOM VARIABLES ARISING FROM α-CONTINUED FRACTIONS

Abstract

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.