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A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

ESAIM: Probability and Statistics

The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.

A generalized dual maximizer for the Monge–Kantorovich transport problem∗

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

ESAIM: Probability and Statistics

The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic...

A geometry on the space of probabilities (I). The finite dimensional case.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω = [1,n] or on P = {p = (p1, ..., pn) ∈ Rn| pi > 0; Σi=1n pi = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in Cn.

A geometry on the space of probabilities (II). Projective spaces and exponential families.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...

A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications

Bianca Satco (2006)

Czechoslovak Mathematical Journal

This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.

Currently displaying 61 – 80 of 2105