Compound Poisson approximation

V. Čekanavičius; S. Y. Novak

doi:10.1214/22-PS8

2022 Compound Poisson approximation

V. Čekanavičius, S. Y. Novak

Author Affiliations +

Probab. Surveys 19: 271-350 (2022). DOI: 10.1214/22-PS8

Abstract

We overview the results on the topic of compound Poisson approximation to the distribution of a sum $\hspace{0.1667em}{S_{n}}={X_{1}}+\cdots +{X_{n}}\hspace{0.1667em}$ of (possibly dependent) random variables. We indicate a number of open problems and discuss directions of further research.

Funding Statement

S. Y. Novak was supported by the Engineering and Physical Sciences Research Council [grant number EP/W010607/1].

Acknowledgments

The authors are grateful to the referee for helpful remarks.

Citation

Download Citation

V. Čekanavičius. S. Y. Novak. "Compound Poisson approximation." Probab. Surveys 19 271 - 350, 2022. https://doi.org/10.1214/22-PS8

Information

Received: 1 August 2021; Published: 2022

First available in Project Euclid: 2 May 2022

MathSciNet: MR4416129

Digital Object Identifier: 10.1214/22-PS8

Subjects:

Primary: 60E15 , 60F05 , 60G50 , 60G51 , 60G55 , 60G70 , 60J75

Secondary: 62E17 , 62E20

Keywords: compound Poisson approximation , Gini–Kantorovich distance , Kolmogorov’s problem , signed compound Poisson measure , total variation distance

Rights: Creative Commons Attribution 4.0 International License.

Access the abstract

JOURNAL ARTICLE
80 PAGES

DOWNLOAD PDF + SAVE TO MY LIBRARY