Mean field control with absorption
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916009978363904 |
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| author | Cardaliaguet, Pierre Jackson, Joe Souganidis, Panagiotis E. |
| author_facet | Cardaliaguet, Pierre Jackson, Joe Souganidis, Panagiotis E. |
| contents | In this paper we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are coupled through their boundary conditions. The value function of the limiting problem; meanwhile, solves a Hamilton-Jacobi equation set on the space of sub-probability measures on the smooth domain, i.e. the space of non-negative measures with total mass at most one. Our main contributions are (i) to establish a comparison principle for this novel infinite-dimensional Hamilton-Jacobi equation and (ii) to prove that the value of the N-particle problem converges in a suitable sense towards the value of the limiting problem as N tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean field control with absorption Cardaliaguet, Pierre Jackson, Joe Souganidis, Panagiotis E. Analysis of PDEs Optimization and Control Probability In this paper we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are coupled through their boundary conditions. The value function of the limiting problem; meanwhile, solves a Hamilton-Jacobi equation set on the space of sub-probability measures on the smooth domain, i.e. the space of non-negative measures with total mass at most one. Our main contributions are (i) to establish a comparison principle for this novel infinite-dimensional Hamilton-Jacobi equation and (ii) to prove that the value of the N-particle problem converges in a suitable sense towards the value of the limiting problem as N tends to infinity. |
| title | Mean field control with absorption |
| topic | Analysis of PDEs Optimization and Control Probability |
| url | https://arxiv.org/abs/2509.07877 |