Regularity of the Schrödinger cost.

Gauthier Clerc (1)

1 EDPA - Équations aux dérivées partielles, analyse

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.

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Gauthier Clerc. Regularity of the Schrödinger cost.. ESAIM: Control, Optimisation and Calculus of Variations, 2022, 28, pp.48. ⟨10.1080/00036811.2022.2103679⟩. ⟨hal-03196058v2⟩