ABSTRACT
In this chapter, we study the approximation of copulas by means of different subclasses and by using different kinds of convergence. Pros and cons of each method will be discussed.
4.1 Uniform approximations of copulas
Here we present three different methods to approximate (in the L∞-norm) a copula. Specifically, given a copulaC ∈ Cd, possible ways are determined to find a sequence (Cn)n∈N ⊂ Cd such that, as n goes to∞, Cn tends to C uniformly. We recall that, under this kind of convergence, the space of copulas Cd is complete and compact (Theorem 1.7.7).
