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Journal of Mathematical Sciences

, Volume 244, Issue 5, pp 771–778 | Cite as

Rare Events and Poisson Point Processes

  • F. GötzeEmail author
  • A. Yu. Zaitsev
Article
  • 4 Downloads

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates for the closeness between the sample containing independent observations of rare events and the Poisson point process which is obtained after a Poissonization of the initial sample.

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© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Universität Bielefeld, Germany and St. Petersburg Department of Steklov Mathematical InstituteSt.Petersburg State UniversitySt.PetersburgRussia

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