title: On inequalities for conditional probabilities of unions of events and the conditional Borel—Cantelli lemma
metadata.name: dc.contributor.author
metadata.value: Frolov, Andrei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-01-05T18:12:20Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-01-05T18:12:20Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Frolov A. N. On inequalities for conditional probabilities of unions of events and the conditional Borel—Cantelli lemma. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 651–662.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.415
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/5906
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We derive new upper and lower bounds for conditional (given σ-field A) probabilities of unions of events.
  These bounds are sharp. Taking of expectations from left-hand and right-hand sides of such inequalities
  may yield better bounds than a direct estimation of probabilities of events. An example is given. We
  also derive new generalizations of the conditional Borel—Cantelli lemma. Taking of expectations, one can
  obtain new variants of the Borel—Cantelli lemma under conditions that differ from classical ones. Refs 11.
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Bonferroni inequalities
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: probabilities of unions of events
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: conditional Borel—Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Borel—Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On inequalities for conditional probabilities of unions of events and the conditional Borel—Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15-Frolov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/5906/1/15-Frolov.pdf
resources.format: Adobe PDF
resources.size: 264,17 kB