Transposition Approach to Optimal Control of McKean-Vlasov SPDEs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918375652851712 |
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| author | Chen, Liangying Stannat, Wilhelm |
| author_facet | Chen, Liangying Stannat, Wilhelm |
| contents | In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a Pontryagin-type stochastic maximum principle that provides necessary optimality conditions for admissible controls. The analysis is based on the classical spike variation method together with the introduction of an adjoint backward stochastic partial differential equation involving Lions derivatives with respect to probability measures. Our results extend the stochastic maximum principle for McKean-Vlasov controlled stochastic differential equations to the infinite-dimensional SPDE setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transposition Approach to Optimal Control of McKean-Vlasov SPDEs Chen, Liangying Stannat, Wilhelm Probability Optimization and Control 93E20, 60H15 In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a Pontryagin-type stochastic maximum principle that provides necessary optimality conditions for admissible controls. The analysis is based on the classical spike variation method together with the introduction of an adjoint backward stochastic partial differential equation involving Lions derivatives with respect to probability measures. Our results extend the stochastic maximum principle for McKean-Vlasov controlled stochastic differential equations to the infinite-dimensional SPDE setting. |
| title | Transposition Approach to Optimal Control of McKean-Vlasov SPDEs |
| topic | Probability Optimization and Control 93E20, 60H15 |
| url | https://arxiv.org/abs/2603.06245 |