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January, 2021 Regularity of Schrödinger's functional equation in the weak topology and moment measures
Toshio MIKAMI
J. Math. Soc. Japan 73(1): 99-123 (January, 2021). DOI: 10.2969/jmsj/81928192

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.

Funding Statement

This work was supported by JSPS KAKENHI Grant Numbers JP26400136 and JP16H03948.

Citation

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Toshio MIKAMI. "Regularity of Schrödinger's functional equation in the weak topology and moment measures." J. Math. Soc. Japan 73 (1) 99 - 123, January, 2021. https://doi.org/10.2969/jmsj/81928192

Information

Received: 3 January 2019; Revised: 29 August 2019; Published: January, 2021
First available in Project Euclid: 26 May 2020

Digital Object Identifier: 10.2969/jmsj/81928192

Subjects:
Primary: 60G30
Secondary: 93E20

Keywords: moment measure , regularity , Schrödinger's functional equation , stochastic optimal transportation

Rights: Copyright © 2021 Mathematical Society of Japan

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Vol.73 • No. 1 • January, 2021
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