title: On bounds for convergence rates in combinatorial strong limit theorems and its applications
metadata.name: dc.contributor.author
metadata.value: Frolov, Andrei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-21T19:38:16Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-21T19:38:16Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Frolov А. N. On bounds for convergence rates in combinatorial strong limit theorems and its applications. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 688–698.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.410
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21919
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We find necessary and sufficient conditions for convergences of series of weighted probabilities of large deviations for combinatorial sums
  i Xniπn(i), where  Xnij  is a matrix
  of order n of independent random variables and (πn(1), πn(2),...,πn(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2,...,n,
  independent with Xnij . We obtain combinatorial variants of results on convergence rates
  in the strong law of large numbers and the law of the iterated logarithm under conditions
  closed to optimal ones. We discuss applications to rank statistics.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by Russian Foundation for Basic Research (grant no. 18-01-00393).
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: combinatorial sums
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convergence rate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: law of the iterated logarithm
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong law of large numbers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Baum — Katz bounds
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: combinatorial strong law of large numbers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: combinatorial law of the iterated logarithm
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rank statistics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Spearman’s coefficient of rank correlation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On bounds for convergence rates in combinatorial strong limit theorems and its applications
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 688-698.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21919/1/688-698.pdf
resources.format: Adobe PDF
resources.size: 317,14 kB