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Convergence results for patchwork copulas. (English) Zbl 1346.60007

Summary: We present a general construction that allows to extend a given subcopula to a copula in such a way that the extension is affine on some specific segments of the copula domain. This construction is hence applied to provide convergence theorems for approximating a copula in strong convergence and in \(D_{1}\)-metric (related to the Markov kernel representation of a copula).

MSC:

60E05 Probability distributions: general theory
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