Moments and associated measures of copulas with fractal support

摘要

Copulas are closely related to the study of distributions and the dependence between random variables. In this paper we develop a recurrence formula for the moments of a measure associated with a copula (a bivariate distribution function with uniform one-dimensional marginals) in the case that its support is a fractal set. We do the same for its principal and secondary diagonals. We also study certain measures of dependence or association for these copulas with fractal supports.