[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170297

TYPE SPACES AND WASSERSTEIN SPACES

Song, Shichang (Department of Mathematics Beijing Jiaotong University)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 447-469 More about this Journal

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.

Keywords

random variables; type spaces; Wasserstein distances;

Citations & Related Records

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