SOME STRONG MIXING PROPERTIES OF A SEQUENCE OF RANDOM VARIABLES ARISING FROM α-CONTINUED FRACTIONS
2003 ◽
Vol 03
(04)
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pp. 463-476
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Keyword(s):
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.
2012 ◽
Vol 396
(1)
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pp. 1-6
1993 ◽
Vol 03
(04)
◽
pp. 1045-1049
1996 ◽
Vol 06
(06)
◽
pp. 1143-1151
2012 ◽
Vol 33
(2)
◽
pp. 529-548
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1996 ◽
Vol 16
(4)
◽
pp. 735-749
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2009 ◽
Vol 29
(4)
◽
pp. 1185-1215
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