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

Autor:	De Vecchi, Francesco C., Rigoni, Chiara
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Analysis of PDEs Mathematics - Optimization and Control Primary: 49N80 93E20 49Q22 Secondary: 60H10 65C35
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
Externí odkaz:	http://arxiv.org/abs/2405.12960 Zobrazit plný text záznamu View this record from Arxiv