×

Idempotent copulas with fractal support. (English) Zbl 1252.37073

Greco, Salvatore (ed.) et al., Advances in computational intelligence. 14th international conference on information processing and management of uncertainty in knowledge-based systems, IPMU 2012, Catania, Italy, July 9–13, 2012. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-31714-9/pbk; 978-3-642-31715-6/ebook). Communications in Computer and Information Science 298, 161-170 (2012).
Summary: In [Insur. Math. Econ. 37, No. 1, 42–48 (2005; Zbl 1098.60018)], G. A. Fredricks, R. B. Nelsen and J. A. Rodríguez-Lallena showed that certain iterated function systems (IFS) can be used to construct copulas with fractal support. Since, firstly, the same construction also works with respect to the \(D_1\)-metric on the space of copulas which is much stronger than the uniform metric and, secondly, the star product of copulas is (jointly) continuous with respect to this metric the IFS approach can also be used to construct idempotent copulas with fractal support. The main result of the paper is that for each open interval \(I\subseteq [1,2]\) there exists an idempotent copula A such that the Hausdorff dimension of the support of \(A\) is contained in the interval \(I\).
For the entire collection see [Zbl 1251.68016].

MSC:

37N40 Dynamical systems in optimization and economics
37E05 Dynamical systems involving maps of the interval
60E05 Probability distributions: general theory

Citations:

Zbl 1098.60018
PDFBibTeX XMLCite
Full Text: DOI