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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 4, Pages 678–687
DOI: https://doi.org/10.21638/spbu01.2020.409 (Mi vspua155) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Limit theorems for generalized perimeters of random inscribed polygons. I

E. N. Simarovaab

a St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b Leonhard Euler International Mathematical Institute, 29B, 14 liniya V. O., St. Petersburg, 199178, Russian Federation
Full-text PDF (313 kB) Citations (2)
DOI: https://doi.org/10.21638/spbu01.2020.409
Abstract: Lao and Mayer (2008) recently developed the theory of U-max-statistics, where instead of the usual averaging the values of the kernel over subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. Their limit distributions are related to distributions of extreme values. This is the first article devoted to the study of the generalized perimeter (the sum of side powers) of an inscribed random polygon, and of U-max-statistics associated with it. It describes the limiting behavior for the extreme values of the generalized perimeter. This problem has not been studied in the literature so far. One obtains some limit theorems in the case when the parameter y, arising in the definition of the generalized perimeter does not exceed 1.
Keywords: U-max-statistics, Poisson approximation, generalized perimeter, limiting behavior.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1619
The work is supported by Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1619).
Received: 05.03.2020
Revised: 18.05.2020
Accepted: 18.07.2020
English version:
Vestnik St. Petersburg University, Mathematics, 2020, Volume 7, Issue 4, Pages 434–442
DOI: https://doi.org/10.1134/S1063454120040093
Document Type: Article
UDC: 519.224
MSC: 60D05, 60F05, 60G70
Language: Russian
Citation: E. N. Simarova, “Limit theorems for generalized perimeters of random inscribed polygons. I”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:4 (2020), 678–687; Vestn. St. Petersbg. Univ., Math., 7:4 (2020), 434–442
Citation in format AMSBIB
\Bibitem{Sim20}
\by E.~N.~Simarova
\paper Limit theorems for generalized perimeters of random inscribed polygons. I
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 4
\pages 678--687
\mathnet{http://mi.mathnet.ru/vspua155}
\crossref{https://doi.org/10.21638/spbu01.2020.409}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2020
\vol 7
\issue 4
\pages 434--442
\crossref{https://doi.org/10.1134/S1063454120040093}
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