Control on Hilbert Space and Mean Field Control: the Common Noise Case
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929709500071936 |
|---|---|
| author | Bensoussan, Alain Graber, P. Jameson Yam, Phillip |
| author_facet | Bensoussan, Alain Graber, P. Jameson Yam, Phillip |
| contents | The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \cite{CDLL}, following the approach of control on Hilbert spaces introduced by the authors in \cite{BGY-2}. We include the common noise in this paper, so the alternative is now complete. Since we consider a control problem, our theory applies only to Mean field control and not to mean field games. The assumptions are adapted to guarantee a unique optimal control, so they insure that the cost functional is strictly convex and coercive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Control on Hilbert Space and Mean Field Control: the Common Noise Case Bensoussan, Alain Graber, P. Jameson Yam, Phillip Optimization and Control Analysis of PDEs 49N80 The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \cite{CDLL}, following the approach of control on Hilbert spaces introduced by the authors in \cite{BGY-2}. We include the common noise in this paper, so the alternative is now complete. Since we consider a control problem, our theory applies only to Mean field control and not to mean field games. The assumptions are adapted to guarantee a unique optimal control, so they insure that the cost functional is strictly convex and coercive. |
| title | Control on Hilbert Space and Mean Field Control: the Common Noise Case |
| topic | Optimization and Control Analysis of PDEs 49N80 |
| url | https://arxiv.org/abs/2502.07051 |