A semigroup approach to Poisson approximation with respect to the point metric (Q1903178)

Let \(X_1, \ldots, X_n\) be independent Bernoulli random variables. The article compares the distribution of \(S_n = \sum^n_{j = 1} X_j\) with suitable Poisson distributions, using as measure of discrepancy the largest difference between two point probabilities. Sharp asymptotic formulae for the discrepancy are derived, using the operator approach of \textit{P. Deheuvels} and \textit{D. Pfeifer} [Ann. Probab. 14, 663-676 (1986; Zbl 0597.60019)].