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The paper investigates the Hoeffding-Sobol decomposition of homogeneous co-survival functions. For this class of functions, the spectral representation is transfered to the terms of the functional decomposition, and in addition to their individual variances or superset combinations. Such formulae make it possible to derive bounds for the tail dependograph.; Cet article étudie la décomposition de Hoeffding--Sobol des co-survival fonctions homogènes. Pour cette classe de fonctions, la représentation spectrale est transférée aux termes de la décomposition fonctionnelle, et également aux variances individuelles ou combinaisons sur les sur-ensembles. De telles formules permettent de déduire des bornes pour le tail dependograph.

The paper investigates the Hoeffding-Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transfered to the terms of the functional decomposition, and in addition to their individual variances, or to the superset combinations of those. The domain of integration in the resulting formulae is reduced in comparison with the already known expressions. When the function under study is the stable tail dependence function of a random vector, ranking these superset indices corresponds to cluster the components of the random vector with respect to their asymptotic dependence. Their Choquet representation is the main ingredient in deriving a sharp upper bound for the quantities involved in the tail dependograph, a graph in extreme value theory that summarizes asymptotic dependence.; The paper investigates the Hoeffding-Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transfered to the terms of the functional decomposition, and in addition to their individual variances, or to the superset combinations of those. The domain of integration in the resulting formulae is reduced in comparison with the already known expressions. When the function under study is the stable tail dependence function of a random vector, ranking these superset indices corresponds to cluster the components of the random vector with respect to their asymptotic dependence. Their Choquet representation is the main ingredient in deriving a sharp upper bound for the quantities involved in the tail dependograph, a graph in extreme value theory that summarizes asymptotic dependence.