Some remarks on a probability limit theorem for continued fractions

Samur, Jorge

doi:10.1090/S0002-9947-96-01571-1

Some remarks on a probability limit theorem for continued fractions
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Trans. Amer. Math. Soc. 348 (1996), 1411-1428 Request permission

Abstract:

It is shown that if a certain condition on the variances of the partial sums is satisfied then a theorem of Philipp and Stout, which implies the asymptotic fluctuation results known for independent random variables, can be applied to some quantities related to continued fractions. Previous results on the behavior of the approximation by the continued fraction convergents to a random real number are improved.

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