Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TYPE SPACES AND WASSERSTEIN SPACES

  • Song, Shichang (Department of Mathematics Beijing Jiaotong University)
  • Received : 2017.05.03
  • Accepted : 2017.06.26
  • Published : 2018.03.01
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Abstract

Types (over parameters) in the theory of atomless random variable structures correspond precisely to (conditional) distributions in probability theory. Moreover, the logic (resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) convergence of distributions. In this paper, we study metrics between types. We show that type spaces under $d^{\ast}-metric$ are isometric to Wasserstein spaces. Using optimal transport theory, two formulas for the metrics between types are given. Then, we give a new proof of an integral formula for the Wasserstein distance, and generalize some results in optimal transport theory.

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Acknowledgement

Supported by : National Natural Science Fund of China

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