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A1034
Title: Convergence of copulas revisited: Different notions of convergence and their interrelations Authors:  Nicolas Dietrich - Universität Salzburg (Austria) [presenting]
Juan Fernandez Sanchez - Universidad de Almeria (Spain)
Wolfgang Trutschnig - University of Salzburg (Austria)
Abstract: Building upon the one-to-one relation between the family $\mathcal{C}$ of bivariate copulas and Markov operators we consider the metric $OP_p$ corresponding to the $L_p$, $p \in[1\infty]$ operator norm and study its interrelation with other metrics on $\mathcal{C}$. In particular, we prove the surprising result that $OP_1$ convergence implies weak conditional convergence of the transposed copulas and establish the fact that the topology induced by $OP_\infty$ is strictly finer than the topology induced by weak conditional convergence.