A description based on optimal transport for a class of stochastic McKean-Vlasov control problems
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914804093943808 |
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| author | De Vecchi, Francesco C. Rigoni, Chiara |
| author_facet | De Vecchi, Francesco C. Rigoni, Chiara |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12960 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A description based on optimal transport for a class of stochastic McKean-Vlasov control problems De Vecchi, Francesco C. Rigoni, Chiara Probability Analysis of PDEs Optimization and Control Primary: 49N80, 93E20, 49Q22, Secondary: 60H10, 65C35, 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. |
| title | A description based on optimal transport for a class of stochastic McKean-Vlasov control problems |
| topic | Probability Analysis of PDEs Optimization and Control Primary: 49N80, 93E20, 49Q22, Secondary: 60H10, 65C35, |
| url | https://arxiv.org/abs/2405.12960 |