A limit theory for controlled McKean-Vlasov SPDEs
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911695025209344 |
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| author | Criens, David |
| author_facet | Criens, David |
| contents | We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a set-valued propagation of chaos result which shows that sets of empirical distributions converge to sets of mean field limits in the Hausdorff metric topology. Further, we discuss limit theorems related to stochastic optimal control theory. To illustrate our findings, we apply them to a controlled interacting particle system of stochastic porous media equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00928 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A limit theory for controlled McKean-Vlasov SPDEs Criens, David Probability Analysis of PDEs Optimization and Control We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a set-valued propagation of chaos result which shows that sets of empirical distributions converge to sets of mean field limits in the Hausdorff metric topology. Further, we discuss limit theorems related to stochastic optimal control theory. To illustrate our findings, we apply them to a controlled interacting particle system of stochastic porous media equations. |
| title | A limit theory for controlled McKean-Vlasov SPDEs |
| topic | Probability Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2310.00928 |