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Wasserstein Derivatives.pdf

WZ-derivative.pdf
Preview of Wasserstein Derivatives
🔗 Source: dornsife.usc.edu
📊 Size: 86 KB
📄 Pages: 3 pages
⬇️ Downloads: 192

Summary

An elementary proof is provided for the structure of Wasserstein derivatives, specifically that DF(ξ) = g(ξ), where g is a deterministic function depending only on the law of ξ, for a law-invariant and continuously Fréchet differentiable mapping F. The proof first considers the case where ξ is discrete and then extends to the general case using a limiting argument. The result is shown to hold for any random variable ξ with the same law, and the function g is demonstrated to depend only on the law of ξ.

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Description

An elementary proof is provided for the structure of Wasserstein derivatives, specifically that DF(ξ) = g(ξ), where g is a deterministic function depending...

Technical Information

  • File Format: PDF
  • File Size: 86 KB
  • Pages: 3
  • Language: EN
  • Total Downloads: 192
  • Last Updated: 1 week ago

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