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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Some remarks on a probability limit theorem
for continued fractions


Author: Jorge D. Samur
Journal: Trans. Amer. Math. Soc. 348 (1996), 1411-1428
MSC (1991): Primary 11K50, 60F17; Secondary 11K60, 60F05, 60F15
DOI: https://doi.org/10.1090/S0002-9947-96-01571-1
MathSciNet review: 1344212
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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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Additional Information

Jorge D. Samur
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Casilla de correo 172, 1900 La Plata, Argentina
Email: jorge@mate.unlp.edu.ar

DOI: https://doi.org/10.1090/S0002-9947-96-01571-1
Keywords: Continued fractions, approximation by the principal convergents, almost sure invariance principle
Received by editor(s): January 1, 1995
Additional Notes: Some results were announced at the 8th International Conference on Probability in Banach Spaces, Brunswick, Maine, July 1991.
Article copyright: © Copyright 1996 American Mathematical Society