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Optimal multiphase transportation with prescribed momentum

Yann Brenier, Marjolaine Puel (2002)

ESAIM: Control, Optimisation and Calculus of Variations

A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.

Optimal Multiphase Transportation with prescribed momentum

Yann Brenier, Marjolaine Puel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.

Optimal nonlinear transformations of random variables

Aldo Goia, Ernesto Salinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....

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