Poisson approximation for the number of large digits of inhomogeneousf-expansions |
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Authors: | Lothar Heinrich |
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Affiliation: | (1) Fakultät für Mathematik und Informatik Institut für Stochastik, TU Bergakademie Freiberg, Bernhard-von-Cotta-Str. 2, D-09596 Freiberg (Sachsen), Germany |
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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 levelLn 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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Keywords: | 60F05 60F10 60K05 10F20 |
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