- Probab. Surveys
- Volume 16 (2019), 228-276.
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.
Probab. Surveys, Volume 16 (2019), 228-276.
Received: November 2018
First available in Project Euclid: 14 August 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks 60G51: Processes with independent increments; Lévy processes 60G55: Point processes 60G70: Extreme value theory; extremal processes 60J75: Jump processes 62E17: Approximations to distributions (nonasymptotic) 62E20: Asymptotic distribution theory
Novak, S. Y. Poisson approximation. Probab. Surveys 16 (2019), 228--276. doi:10.1214/18-PS318. https://projecteuclid.org/euclid.ps/1565748164