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 language | English |
|---|---|
| Pages (from-to) | 39-52 |
| Number of pages | 14 |
| Journal | International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems |
| Volume | 18 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 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