Regularity of Schrödinger's functional equation in the weak topology and moment measures

2018/12/28 by Toshio Mikami, Mikami, Toshio
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G30 (Primary) #93E20 (Secondary) #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1812.10908

openalex publication_date 2018/12/28 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28

Abstract

We study the continuity and the measurability of the solution to Schrödinger's functional equation, with respect to space, kernel and marginals, provided the space of all Borel probability measures is endowed with the weak topology. This is a continuation of our previous result where the space of all Borel probability measures was endowed with the strong topology. As an application, we construct a convex function of which the moment measure is a given probability measure, by the zero noise limit of a class of stochastic optimal transportation problems.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions
• On the difference between entropic cost and the optimal transport cost

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