Tokyo Journal of Mathematics

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

Gabriela Ileana SEBE

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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

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

First available in Project Euclid: 31 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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