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This œuvre, Barycenter in Wasserstein space existence and consistency, by Jean-michel Loubes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

Barycenter in Wasserstein space existence and consistency


Barycenter in Wasserstein space existence and consistency
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We study barycenters in the Wasserstein space Pp(E) of a locally compact geodesic space (E, d). In this framework, we define the barycenter of a measure ℙ on Pp(E) as its Fréchet mean. The paper establishes its existence and states consistency with respect to ℙ. We thus extends previous results on ℝ d , with conditions on ℙ or on the sequence converging to ℙ for consistency.
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Barycenter in Wasserstein space existence and consistency
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