We overview results on the topic of Poisson approximation that are missed in existing surveys. The main attention is paid to the problem of Poisson approximation to the distribution of a sum of Bernoulli and, more generally, non-negative integer-valued random variables.
We do not restrict ourselves to a particular method, and overview the whole range of issues including the general limit theorem, estimates of the accuracy of approximation, asymptotic expansions, etc. Related results on the accuracy of compound Poisson approximation are presented as well.
We indicate a number of open problems and discuss directions of further research.
"Poisson approximation." Probab. Surveys 16 228 - 276, 2019. https://doi.org/10.1214/18-PS318