A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems
The work concerns about multiscale McKean–Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of these systems and establish a limit theorem about nonlinear filt...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.637/ |
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| _version_ | 1825206200084463616 |
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| author | Qiao, Huijie Zhu, Shengqing |
| author_facet | Qiao, Huijie Zhu, Shengqing |
| author_sort | Qiao, Huijie |
| collection | DOAJ |
| description | The work concerns about multiscale McKean–Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of these systems and establish a limit theorem about nonlinear filtering of them in the $L^2$ sense. |
| format | Article |
| id | doaj-art-f04a3e443f2746698504014db7f645bd |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-f04a3e443f2746698504014db7f645bd2025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111287129910.5802/crmath.63710.5802/crmath.637A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systemsQiao, Huijie0Zhu, Shengqing1School of Mathematics, Southeast University, Nanjing, Jiangsu 211189, P.R.ChinaSchool of Mathematics, Southeast University, Nanjing, Jiangsu 211189, P.R.ChinaThe work concerns about multiscale McKean–Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of these systems and establish a limit theorem about nonlinear filtering of them in the $L^2$ sense.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.637/Multiscale McKean–Vlasov stochastic systemsaverage principlenonlinear filteringlimit theorem |
| spellingShingle | Qiao, Huijie Zhu, Shengqing A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems Comptes Rendus. Mathématique Multiscale McKean–Vlasov stochastic systems average principle nonlinear filtering limit theorem |
| title | A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems |
| title_full | A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems |
| title_fullStr | A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems |
| title_full_unstemmed | A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems |
| title_short | A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems |
| title_sort | limit theorem of nonlinear filtering for multiscale mckean vlasov stochastic systems |
| topic | Multiscale McKean–Vlasov stochastic systems average principle nonlinear filtering limit theorem |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.637/ |
| work_keys_str_mv | AT qiaohuijie alimittheoremofnonlinearfilteringformultiscalemckeanvlasovstochasticsystems AT zhushengqing alimittheoremofnonlinearfilteringformultiscalemckeanvlasovstochasticsystems AT qiaohuijie limittheoremofnonlinearfilteringformultiscalemckeanvlasovstochasticsystems AT zhushengqing limittheoremofnonlinearfilteringformultiscalemckeanvlasovstochasticsystems |