Abstract
We provide two families of lower bounds for theL 2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.
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Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.
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Cuesta-Albertos, J.A., Matrán-Bea, C. & Tuero-Diaz, A. On lower bounds for theL 2-Wasserstein metric in a Hilbert space. J Theor Probab 9, 263–283 (1996). https://doi.org/10.1007/BF02214649
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DOI: https://doi.org/10.1007/BF02214649