A description based on optimal transport for a class of stochastic McKean-Vlasov control problems
Autor: | De Vecchi, Francesco C., Rigoni, Chiara |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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 Schr\"odinger 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. Comment: 54 pages. Comments are welcome! |
Databáze: | arXiv |
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