A Monotone Approximation to the Wasserstein Diffusion

Karl-Theodor Sturm ()
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Karl-Theodor Sturm: Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Angewandte Mathematik

A chapter in Singular Phenomena and Scaling in Mathematical Models, 2014, pp 25-48 from Springer

Abstract: Abstract The Wasserstein space $$\mathcal{P}(M)$$ on an Euclidean or Riemannian space M – i.e. the space of probability measures on M equipped with the L 2-Wasserstein distance d W – offers a rich geometric structure. This allows to develop a far reaching first order calculus, with striking applications for instance to the reformulation of conservative PDEs on M as gradient flows of suitable functionals on $$\mathcal{P}(M)$$ , see e.g. [1, 7, 11].

Keywords: Conservative PDEs; Rich Geometric Structure; Striking Application; Wasserstein Space; Dirichlet Form (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-00786-1_2

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DOI: 10.1007/978-3-319-00786-1_2

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