Imprecise copulas and bivariate stochastic orders

Sklar's theorem is an important tool that connects bidimensional distribution functions to their marginals by means of a copula. When there is imprecision about the marginal models, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision.