Poisson approximation for the number of large digits of inhomogeneous f-expansions

We determine the exact rate of Poisson approximation and give a second-order Poisson-Charlier expansion for the number of excedances of a given level L-n 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.