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Lindner, Alexander M. and Szimayer, Alexander (2005): A Limit Theorem for Copulas. Collaborative Research Center 386, Discussion Paper 433
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Abstract

We characterize convergence of a sequence of d-dimensional random vectors by convergence of the one-dimensional margins and of the copula. The result is applied to the approximation of portfolios modelled by t-copulas with large degrees of freedom, and to the convergence of certain dependence measures of bivariate distributions.