title: Limit theorems for generalized perimeters of random inscribed polygons
metadata.name: dc.contributor.author
metadata.value: Simarova, Ekaterina N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-21T19:32:53Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-21T19:32:53Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Simarova E. N. Limit theorems for generalized perimeters of random inscribed polygons. I. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 678–687.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.409
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21918
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Ministry of Science and Higher Education of the Russian Federation
  (agreement no. 075-15-2019-1619).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: U-max-statistics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Poisson approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized perimeter
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: limiting behavior
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Limit theorems for generalized perimeters of random inscribed polygons
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 678-687.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21918/1/678-687.pdf
resources.format: Adobe PDF
resources.size: 315,71 kB