On a Formula for the L2 Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

✍ Scribed by Matthias Gelbrich

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 819 KB
• Volume: 147
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19901470121

✦ Synopsis

Abstract

For a separable metric space (X, d) L^p^ Wasserstein metrics between probability measures μ and v on X are defined by
where the infimum is taken over all probability measures η on X × X with marginal distributions μ and v, respectively. After mentioning some basic properties of these metrics as well as explicit formulae for X = R a formula for the L^2^ Wasserstein metric with X = R^n^ will be cited from [5], [9], and [21] and proved for any two probability measures of a family of elliptically contoured distributions.

Finally this result will be generalized for Gaussian measures to the case of a separable Hilbert space.