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

Weihua Yang, Xu Zhang () and Xia Wang
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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

Mathematics, 2024, vol. 12, issue 15, 1-13

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.

Keywords: Wasserstein metric; optimal matching; random variable; Poisson process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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