Poisson approximation for the number of large digits of inhomogeneousf-expansions

Abstract

Abstract.We determine the exact rate of Poisson approximation and give a second-order PoissonCharlier expansion for the number of excedances of a given level Ln among the first n digits of inhomogeneous f-expansions of real numbers in the unit interval. The application of this general result to homogeneous f-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.