| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 48 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2022033 | |
| Published online | 07 July 2022 | |
Regularity properties of the Schrödinger cost
Institut Camille Jordan, Umr Cnrs 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
* Corresponding author: clerc@math.univ-lyon1.fr
Received:
12
April
2021
Accepted:
19
April
2022
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.
Mathematics Subject Classification: 35K05
Key words: Schrödinger problem / Otto calculus / Entropy / Benamou-Brenier-Schrödinger formula
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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