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 Probability Surveys > Vol. 16 (2019) open journal systems 


Poisson approximation

S. Y. Novak, MDX University London


Abstract
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well.
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.

AMS 2000 subject classifications: Primary 60E15; secondary 60F05, 60G50, 60G51, 60G55, 60G70, 60J75, 62E17, 62E20.

Keywords: Poisson approximation, compound Poisson approximation, accuracy of approximation, asymptotic expansions, Poisson process approximation, total variation distance, long head runs, long match patterns.

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Novak, S. Y., Poisson approximation, Probability Surveys, 16, (2019), 228-276 (electronic). DOI: 10.1214/18-PS318.

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