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Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 109–119 (Mi znsl6544)  

Rare events and Poisson point processes

F. Götzea, A. Yu. Zaitsevbc

a Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia

Abstract: 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 substantial 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.

Key words and phrases: sums of independent random variables, rare events, Poisson point processes, concentration functions, inequalities.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00367
Saint Petersburg State University СПбГУ--ННИО 6.37.65.2017
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01


Full text: PDF file (199 kB)
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Document Type: Article
UDC: 519.2
Received: 05.12.2017

Citation: F. Götze, A. Yu. Zaitsev, “Rare events and Poisson point processes”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 109–119

Citation in format AMSBIB
\Bibitem{GotZai17}
\by F.~G\"otze, A.~Yu.~Zaitsev
\paper Rare events and Poisson point processes
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 109--119
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6544}


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