Continued fractions, the Chen–Stein method and extreme value theory
نویسندگان
چکیده
منابع مشابه
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Letting x = [a1(x), a2(x), . . .] denote the continued fraction expansion of an irrational number x ∈ (0, 1), Khinchin proved that Sn(x) = ∑n k=1 ak(x) ∼ 1 log 2 n logn in measure, but not for almost every x. Diamond and Vaaler showed that removing the largest term from Sn(x), the previous asymptotics will hold almost everywhere, showing the crucial influence of the extreme terms of Sn(x) on th...
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where Ed= fl, bkEZ2,, k 2 1, and with some constraints on bk and sk. Usually we will assume that x is irrational, and thus that the expansion (1.1) is infinite. A special case of an SRCF is the regular continuedfraction, RCF, which is obtained by taking ck = 1 for every k in (1.1). The aim in introducing the OCF was to optimize two things simultaneously. In the first place one wishes the conver...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2019
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2019.64