Abstract Formulation of Mean-Field Models and Propagation of Chaos
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915425387806720 |
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| author | Lim, Tau Shean Teoh, Chao Dun |
| author_facet | Lim, Tau Shean Teoh, Chao Dun |
| contents | In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory. This allows for the inclusion of a wider range of mean-field particle systems within a unified structure. This new approach involves: (1) constructing an abstract framework using semigroups and generators; (2) formulating a corresponding mean-field evolution problem, and proving its well-posedness; (3) demonstrating the propagation of chaos for a class of N-particle systems associated with the mean-field model. Our results are readily applicable to various mean-field models. To demonstrate this, we apply our findings to obtain a new result for Levy-type mean-field systems, which encompass the McKean-Vlasov diffusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abstract Formulation of Mean-Field Models and Propagation of Chaos Lim, Tau Shean Teoh, Chao Dun Analysis of PDEs Probability 60K35, 60J25, 47D07 G.3 In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory. This allows for the inclusion of a wider range of mean-field particle systems within a unified structure. This new approach involves: (1) constructing an abstract framework using semigroups and generators; (2) formulating a corresponding mean-field evolution problem, and proving its well-posedness; (3) demonstrating the propagation of chaos for a class of N-particle systems associated with the mean-field model. Our results are readily applicable to various mean-field models. To demonstrate this, we apply our findings to obtain a new result for Levy-type mean-field systems, which encompass the McKean-Vlasov diffusion. |
| title | Abstract Formulation of Mean-Field Models and Propagation of Chaos |
| topic | Analysis of PDEs Probability 60K35, 60J25, 47D07 G.3 |
| url | https://arxiv.org/abs/2508.02224 |