Regularity properties of the Schrödinger cost
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 48

The Schrödinger problem is an entropy minimisation problem on the space of probability measures. Its optimal value is a cost between two probability measures. In this article we investigate some regularity properties of this cost: continuity with respect to the marginals and time derivative of the cost along probability measures valued curves.

DOI : 10.1051/cocv/2022033
Classification : 35K05
Keywords: Schrödinger problem, Otto calculus, Entropy, Benamou-Brenier-Schrödinger formula 
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     author = {Clerc, Gauthier},
     title = {Regularity properties of the {Schr\"odinger} cost},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {28},
     doi = {10.1051/cocv/2022033},
     mrnumber = {4448806},
     zbl = {1498.49083},
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     url = {https://www.numdam.org/articles/10.1051/cocv/2022033/}
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Clerc, Gauthier. Regularity properties of the Schrödinger cost. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 48. doi: 10.1051/cocv/2022033

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