Regularity of Schrödinger's functional equation in the weak topology and moment measures
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- Mikami Toshio
- Department of Mathematics Tsuda University
Bibliographic Information
- Other Title
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- Regularity of Schrodinger's functional equation in the weak topology and moment measures
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Abstract
<p>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.</p>
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 73 (1), 99-123, 2021
The Mathematical Society of Japan
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Keywords
Details 詳細情報について
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- CRID
- 1390568456354670080
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- NII Article ID
- 130007973744
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 031231316
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed