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

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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>

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Details

  • CRID
    1390568456354670080
  • NII Article ID
    130007973744
  • NII Book ID
    AA0070177X
  • DOI
    10.2969/jmsj/81928192
  • ISSN
    18811167
    18812333
    00255645
  • NDL BIB ID
    031231316
  • Text Lang
    en
  • Data Source
    • JaLC
    • NDL
    • Crossref
    • CiNii Articles
    • KAKEN
  • Abstract License Flag
    Disallowed

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