Tokyo Journal of Mathematics

Convergence Rate for a Continued Fraction Expansion Related to Fibonacci Type Sequences

Gabriela Ileana SEBE

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Abstract

Chan ([2], [3]) considered some continued fraction expansions related to random Fibonacci-type sequences. A Wirsing-type approach to the Perron-Frobenius operator of the associated transformation under its invariant measure allows us to study the optimality of the convergence rate. Actually, we obtain upper and lower bounds of the convergence rate which provide a near-optimal solution to the Gauss-Kuzmin-Lévy problem.

Article information

Source
Tokyo J. Math., Volume 33, Number 2 (2010), 487-497.

Dates
First available in Project Euclid: 31 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1296483483

Digital Object Identifier
doi:10.3836/tjm/1296483483

Mathematical Reviews number (MathSciNet)
MR2779430

Zentralblatt MATH identifier
1227.11094

Subjects
Primary: 11K50: Metric theory of continued fractions [See also 11A55, 11J70]
Secondary: 47B38: Operators on function spaces (general) 60F05: Central limit and other weak theorems

Citation

SEBE, Gabriela Ileana. Convergence Rate for a Continued Fraction Expansion Related to Fibonacci Type Sequences. Tokyo J. Math. 33 (2010), no. 2, 487--497. doi:10.3836/tjm/1296483483. https://projecteuclid.org/euclid.tjm/1296483483


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References

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