Open Access
2019 Poisson approximation
S. Y. Novak
Probab. Surveys 16: 228-276 (2019). DOI: 10.1214/18-PS318


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.


Download Citation

S. Y. Novak. "Poisson approximation." Probab. Surveys 16 228 - 276, 2019.


Received: 1 November 2018; Published: 2019
First available in Project Euclid: 14 August 2019

zbMATH: 1422.60028
MathSciNet: MR3992498
Digital Object Identifier: 10.1214/18-PS318

Primary: 60E15
Secondary: 60F05 , 60G50 , 60G51 , 60G55 , 60G70 , 60J75 , 62E17 , 62E20

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

Vol.16 • 2019
Back to Top