Large deviation principle for a two-time-scale McKean-Vlasov model with jumps
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929195858264064 |
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| author | Yang, Xiaoyu Xu, Yong |
| author_facet | Yang, Xiaoyu Xu, Yong |
| contents | This work focus on the large deviation principle for a two-time scale McKean-Vlasov system with jumps. Based on the variational framework of the McKean-Vlasov system with jumps, it is turned into weak convergence for the controlled system. Unlike general two-time scale system, the controlled McKean-Vlasov system is related to the law of the original system, which causes difficulties in qualitative analysis. In solving this problem, employing asymptotics of the original system and a Khasminskii-type averaging principle together is efficient. Finally, it is shown that the limit is related to the Dirac measure of the solution to the ordinary differential equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviation principle for a two-time-scale McKean-Vlasov model with jumps Yang, Xiaoyu Xu, Yong Probability This work focus on the large deviation principle for a two-time scale McKean-Vlasov system with jumps. Based on the variational framework of the McKean-Vlasov system with jumps, it is turned into weak convergence for the controlled system. Unlike general two-time scale system, the controlled McKean-Vlasov system is related to the law of the original system, which causes difficulties in qualitative analysis. In solving this problem, employing asymptotics of the original system and a Khasminskii-type averaging principle together is efficient. Finally, it is shown that the limit is related to the Dirac measure of the solution to the ordinary differential equation. |
| title | Large deviation principle for a two-time-scale McKean-Vlasov model with jumps |
| topic | Probability |
| url | https://arxiv.org/abs/2401.00671 |