Copulas and associated fractal sets (Q643556)

The authors consider an extension of the problem of constructing copulas whose supports are fractals which has been studied by \textit{G. A. Fredricks}, \textit{R. B. Nelsen} and \textit{J. A. Rodriguez-Lallena} [Insur. Math. Econ. 37, No. 1, 42--48 (2005; Zbl 1098.60018)]. Different types of families of self-similar copulas are investigated using methods from probability and ergodic theory to describe their self-similarity and the self-similarity of their fractal supports. An interesting and unknown example of a copula is given whose support fills the unit square and whose associated measure is concentrated on a set having a Hausdorff dimension less than two. In the last section, examples of copulas with a non-connected support and copulas with totally disconnected supports are constructed.