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
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
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