Abstract
We determine the exact rate of Poisson approximation and give a second-order Poisson-Charlier expansion for the number of excedances of a given levelL n among the firstn digits of inhomogeneousf-expansions of real numbers in the unit interval. The application of this general result to homogeneousf-expansions and, in particular, to regular continued fraction expansions provides not only a generalization but also a strengthening of a classical Poisson limit theorem due to W. Doeblin.
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Heinrich, L. Poisson approximation for the number of large digits of inhomogeneousf-expansions. Monatshefte für Mathematik 124, 237–253 (1997). https://doi.org/10.1007/BF01298246
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DOI: https://doi.org/10.1007/BF01298246