title: On strong forms of the Borel—Cantelli lemma and dynamical systems with polynomial decays of correlations
metadata.name: dc.contributor.author
metadata.value: Frolov, Аndrei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-12-27T14:55:46Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-12-27T14:55:46Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Frolov А.N. On strong forms of the Borel—Cantelli lemma and dynamical systems with polynomial decays of correlations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 4, pp. 644–652. https://doi.org/10.21638/spbu01.2022.407 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.407
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38722
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Strong forms of the Borel—Cantelli lemma are variants of the strong law of large numbers
  for sums of the indicators of events such that the series from probabilities of these events
  diverges. These sums are centered at means and normalized by some function from means.
  In this paper, we derive new strong forms of the Borel—Cantelli lemma under wider restrictions
  on variations of increments of sums than it was done earlier. Strong forms are commonly used for investigations of properties of dynamical systems. We apply our results
  to describe properties of some measure preserving expanding maps of [0, 1] with a fixed
  point at zero. Such results can be proved for similar multidimensional maps as well.
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 9 (67); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: the Borel—Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the quantitative Borel—Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong forms of the Borel—Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: sums of indicators of events
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: almost surely convergence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dynamical systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: polynomial decay of correlations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On strong forms of the Borel—Cantelli lemma and dynamical systems with polynomial decays of correlations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 644-652.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38722/1/644-652.pdf
resources.format: Adobe PDF
resources.size: 296,32 kB