Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures - École polytechnique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures

Résumé

We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new definition of viscosity solutions of this equation, which yields general comparison principles, in particular for cases involving terms modeling stochasticity in the optimal control problem. We are then able to establish results of existence and uniqueness of viscosity solutions of the Hamilton-Jacobi-Bellman equation. These results rely on controllability results for stochastic optimal transport that we also establish.
Fichier principal
Vignette du fichier
sot.pdf (424.38 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04118729 , version 1 (06-06-2023)
hal-04118729 , version 2 (17-05-2024)

Identifiants

Citer

Charles Bertucci. Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures. 2024. ⟨hal-04118729v2⟩
14 Consultations
118 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More