FréChet-Bounds and Their Applications

摘要: This paper gives a review of Frechet-bounds and their applications. In section two an approach to the marginal problem based on duality theory resp. Hahn-Banach theorem is discussed. Main applications concern Strassen representation for stochastic orders, sharpness classical Frechet-bounds, minimal metrics, couplings distributions, Monge-Kantorovic-problem, construction random variables with maximum (resp. minimum) sum variances sum, maximally dependent others. For multivariate systems there useful reduction principle are some bounds simple systems, which yield characterization system dimensional marginals in three-fold product space. three we discuss generalizations Younginequality, solving dual problems Frechet-bounds. A basic notion this connection c-convex functions. As application one can give nice solutions certain transportation problems. We probabilistic proof Young- Oppenheim-inequality. four statistical The Huzurbazar conjecture sufficiency, optimal combination tests question estimation models considered.