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Wasserstein distance on configuration space

Authors
  • Decreusefond, Laurent
Publication Date
Jan 01, 2008
Source
HAL-INRIA
Keywords
Language
English
License
Unknown
External links

Abstract

We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is finite, there exists one unique optimal measure and that this measure is supported by the graph of the derivative (in the sense of the Malliavin calculus) of a ''concave'' (in a sense to be defined below) function. For finite point processes, we give a necessary and sufficient condition for the Wasserstein distance to be finite.

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