Sur les prolongements de sous-copules
The extension of subcopulas is an important domain. One of possible applications is the nonparametric estimation  of a copula: it consists of the smoothing of a subcopula (the empirical copula) while preserving the copulas properties.   In Chapter 2, we present  an extension of the empirical copula based on the tensor product of splines functions. Our estimators are bona fide estimators of the copula.  Chapter 3 tackles the problem of finding all possible extensions of a given subcopula. This subject has been treated in the literature  but these characterizations do not apply on very general spaces. Chapter 4 deals with the following problem: finding the expression of the upper bound of the extensions of a finite subcopula in dimension 3.
copulas subcopulas extensions upper bound density