Imaging with Kantorovich-Rubinstein Discrepancy

Optimal Couplings of Kantorovich-Rubinstein-Wasserstein Lp-distance

The research is supported by Zhejiang Provincial Education Department Research Projects (Y201016421) Abstract We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein Lp−distance (p > 2) (abbreviation: KRW Lp−distance) in a bounded region of Euclidean plane satisfy a partial differential equation. We can also obtain the similar results about Monge-Kantorovich proble...

A Representation for the Kantorovich–rubinstein Distance Defined by the Cameron–martin Norm of a Gaussian Measure on a Banach Space

Extreme points of a ball about a measure with finite support

We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge-Wasserstein and Kantorovich metric balls about a measure whose support has at most n points, consist of measures whose supports have at most n+2 points. Moreover, we use the Strassen and Kantorovich-Rubinstein duality theorems to develop representation...

Coupling on weighted branching trees

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector ...

The Monge-kantorovich Problem for Distributions and Applications

We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace X(Ω) of first order distribution. A particular subclass X♯0(Ω) of such distributions will be considered which includes the infinite sums of dipoles ∑ k(δpk − δnk) studied in [28, 29]. In spite of this weakened regular...