title: On convergence and compactness in variation with shift of discrete probability laws
metadata.name: dc.contributor.author
metadata.value: Alexeev, Ivan A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Khartov, Alexey A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-10-07T11:29:13Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-10-07T11:29:13Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Alexeev I.A., Khartov A.A. On convergence and compactness in variation with shift of discrete probability laws. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 3, pp. 385–393.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/33255
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider a class of discrete distribution functions, whose characteristic functions are separated from zero, i. e. their absolute values are greater than positive constant on the real line. The class is rather wide, because it contains discrete infinitely divisible distribution functions, functions of lattice distributions, whose characteristic functions have no zeroes on the real line, and also distribution functions with a jump greater than 1/2. Recently the authors showed that characteristic functions of elements of this class admit the Lévy-Khinchine type representations with non-monotonic spectral function. Thus our class is included in the set of so called quasi-infinitely divisible distribution functions. Using these representation the authors also obtained limit and compactness theorems with convergence in variation for the sequences from this class. This note is devoted to similar results concerning convergence and compactness but with weakened convergence in variation. Replacing of type of convergence notably expands applicability of the results.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of A.A.Khartov was supported by the joint Russian Foundation for Basic Research and German Research Foundation (grant No. 20-51-12004).
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 8 (66); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: characteristic functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lévy-Khinchine type representations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quasi-infinitely divisible distributions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convergence in variation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: relative compactness
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stochastic compactness
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On convergence and compactness in variation with shift of discrete probability laws
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 385-393.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/33255/1/385-393.pdf
resources.format: Adobe PDF
resources.size: 320,22 kB