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Bivariate copulas: Transformations, asymmetry and measures of concordance

Sebastian Fuchs, Klaus D. Schmidt (2014)

Kybernetika

The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the...

Brownian motion and transient groups

Nicolas Th. Varopoulos (1983)

Annales de l'institut Fourier

In this paper I consider M ˜ M a covering of a Riemannian manifold M . I prove that Green’s function exists on M ˜ if any and only if the symmetric translation invariant random walks on the covering group G are transient (under the assumption that M is compact).

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