Convergence rate for a continued fraction expansion related to Fibonacci type sequences
The author considers some continued fraction expansions related to random Fibonacci-type sequences introduced by \textit{H.-C. Chan} [Fibonacci Q. 44, No. 1, 73--84 (2006; Zbl 1204.11032) and Fibonacci Q. 43, No. 3, 243--255 (2005; Zbl 1081.11010)]. A Wirsing-type approach to the Perron-Frobenius operator of the associated transformation under its invariant measure allows to study the optimality of the convergence rate. Actually, the author obtains upper and lower bounds of the convergence rate which provide a near-optimal solution to the Gauss-Kuzmin-Lévy problem.
scientific article; zbMATH DE number 5869977