Abstract
The main purpose of this paper is to present bounds of the discrepancy between an infinitely divisible distribution function with finite second moment and the normal as well as the poisson distribution function. Special emphasise is put on explicit numerical constancts involved in the error bounds. To improve these estimates an EDGEWORTH expansion in the smooth case and a POISSON–CHARLEIR expansion in the lattice case are developed. Some applications to the POISSON shot noise illustrate the obtained results
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