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The Wasserstein Metric between a Discrete Probability Measure and a Continuous One

Author

Listed:
  • Weihua Yang

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

  • Xu Zhang

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

  • Xia Wang

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

Abstract

This paper examines the Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform measure in the d-dimensional ball, providing an asymptotic estimation of their expectations as n approaches infinity. Furthermore, we investigate this problem within a mixed process framework, where n discrete random variables are generated by the Poisson process.

Suggested Citation

  • Weihua Yang & Xu Zhang & Xia Wang, 2024. "The Wasserstein Metric between a Discrete Probability Measure and a Continuous One," Mathematics, MDPI, vol. 12(15), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2320-:d:1442018
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    References listed on IDEAS

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    1. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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