We study the convergence of an N-particle Markovian controlled system to the solution of some (finite horizon or Schrödinger-type) stochastic McKean-Vlasov control problem. In particular, under suitable assumptions, we prove the convergence of the value functions, of the fixed time probability laws and of the relative entropy in their path space measures. These proofs are based on a Benamou-Brenier type reformulation of the problem and on the superposition principle, both these tools coming from the theory of optimal transport. This is a joint work with Francesco De Vecchi.
Abstract: https://sfb65.univie.ac.at/s/ny/
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