Lipschitz continuity of discrete universal integrals based on copulas

Erich Klement, Anna Kolesárová, Radko Mesiar, Andrea Stupnanová

Research output: Contribution to journalArticlepeer-review

Abstract

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms $L_1$ (Lipschitz stability) and $L_{\infty}$ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization of stochastically increasing Archimedean copulas is also given.
Original languageEnglish
Pages (from-to)39-52
Number of pages14
JournalInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Volume18
Issue number1
DOIs
Publication statusPublished - Feb 2010

Fields of science

  • 101 Mathematics
  • 101004 Biomathematics
  • 101027 Dynamical systems
  • 101013 Mathematical logic
  • 101028 Mathematical modelling
  • 101014 Numerical mathematics
  • 101020 Technical mathematics
  • 101024 Probability theory
  • 102001 Artificial intelligence
  • 102003 Image processing
  • 102009 Computer simulation
  • 102019 Machine learning
  • 102023 Supercomputing
  • 202027 Mechatronics
  • 206001 Biomedical engineering
  • 206003 Medical physics
  • 102035 Data science

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