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arXiv · 2502.07051

Control on Hilbert Space and Mean Field Control: the Common Noise Case

Alain Bensoussan·P. Jameson Graber·Phillip Yam
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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.

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Alain Bensoussan, P. Jameson Graber, Phillip Yam. 2025-02-10. Control on Hilbert Space and Mean Field Control: the Common Noise Case. https://arxiv.org/abs/2502.07051

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