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On a formula for the \(L^ 2\) Wasserstein metric between measures on Euclidean and Hilbert spaces. (English) Zbl 0711.60003

For two normal distributions on \({\mathbb{R}}^ n\) an explicit formula is known for the \(L^ 2\)-metric. From this formula it is clear that the \(L^ 2\)-distance between any two other probability measures is bounded below by the distance between the corresponding normal distributions with the same means and covariances. Furthermore, the same formula holds true for any two distributions which are in a certain affine relation.
In the present paper this condition is exemplified in the case of related elliptically contoured probability measures and an extension is proved to Gaussian measures on Hilbert spaces.
Reviewer: L.Rüschendorf

MSC:

60A10 Probabilistic measure theory
60E05 Probability distributions: general theory
60B11 Probability theory on linear topological spaces
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