The aim of this paper is twofold: first, to show that Poisson approximation problems for independent summands can in a natural way be treated in a suitable operator semigroup framework, allowing at the same time for an asymptotically precise evaluation of the leading term with respect to the total variation distance; second, to determine asymptotically those Poisson distributions which minimize this distance for given Bernoulli summands. Besides semigroup methods, coupling techniques as well as direct computations are used.
"A Semigroup Approach to Poisson Approximation." Ann. Probab. 14 (2) 663 - 676, April, 1986. https://doi.org/10.1214/aop/1176992536