Control on Hilbert Space and Mean Field Control: the Common Noise Case
Optimization and Control
2025-02-12 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.2502.07051,
title = {Control on Hilbert Space and Mean Field Control: the Common Noise Case},
author = {Alain Bensoussan and P. Jameson Graber and Phillip Yam},
journal= {arXiv preprint arXiv:2502.07051},
year = {2025}
}