Bivariate measure-inducing quasi-copulas

Stopar, Nik (author)

It is well known that every bivariate copula induces a positive measure on the Borel $\sigma$-algebra on $\left[0, 1 \right]^2$, but there exist bivariate quasi-copulas that do not induce a signed measure on the same $\sigma$-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.

• Language: English
• Keywords: quasi-copulas, copula, signed measure, total variation norm, infinite series
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 20 str.
• Numbering: Vol. 492, art. 109068
• PID: 20.500.12556/RUL-159795
• UDC: 519.2
• ISSN on article: 0165-0114
• DOI: 10.1016/j.fss.2024.109068
• COBISS.SI-ID: 201999875
• Publication date in RUL: 25.07.2024

Record is a part of a journal

• Title: Fuzzy sets and systems
• Shortened title: Fuzzy sets syst.
• Publisher: Elsevier
• ISSN: 0165-0114
• COBISS.SI-ID: 25498624

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kvazikopula, kopula, predznačena mera, norma totalne variacije, neskončne vrste

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika