Tails of weakly dependent random vectors

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We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mixture models, certain Archimedean copulas and extreme value copulas. The new measure allows to quantify the tail behavior of certain functionals of weakly dependent random vectors at the log scale.