A description based on optimal transport for a class of stochastic McKean-Vlasov control problems

Francesco C. De Vecchi; Chiara Rigoni

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arXiv · 2405.12960

A description based on optimal transport for a class of stochastic McKean-Vlasov control problems

Francesco C. De Vecchi·Chiara Rigoni

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Abstract

We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schrödinger type cost functional. Specifically, under suitable assumptions, we prove the convergence of the value functions, the fixed-time probability distributions, and the relative entropy of their path-space probability laws. These proofs are based on a Benamou-Brenier type reformulation of the problem and a superposition principle, both of which are tools from the theory of optimal transport.

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BibTeX RIS

Francesco C. De Vecchi, Chiara Rigoni. 2024-05-21. A description based on optimal transport for a class of stochastic McKean-Vlasov control problems. https://arxiv.org/abs/2405.12960

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