no. G11
Article de recherche - Probabilités
A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems
[Théorème limite du filtrage non linéaire pour les systèmes stochastiques McKean–Vlasov à plusieurs échelles]
Qiao, Huijie1  ; Zhu, Shengqing1
1School of Mathematics, Southeast University, Nanjing, Jiangsu 211189, P.R.China
Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1287-1299

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.

Ce travail concerne les systèmes stochastiques McKean–Vlasov multi-échelles. Tout d’abord, nous prouvons un principe de moyenne pour ces systèmes au sens L2. De plus, un taux de convergence est présenté. Ensuite, nous définissons le filtrage non linéaire de ces systèmes et établissons un théorème limite sur le filtrage non linéaire de ces systèmes au sens L 2 .

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.637
Classification : 60G35
Keywords: Multiscale McKean–Vlasov stochastic systems, average principle, nonlinear filtering, limit theorem

Qiao, Huijie  1   ; Zhu, Shengqing  1

1 School of Mathematics, Southeast University, Nanjing, Jiangsu 211189, P.R.China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Qiao, Huijie and Zhu, Shengqing},
     title = {A limit theorem of nonlinear filtering for multiscale {McKean{\textendash}Vlasov} stochastic systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1287--1299},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     number = {G11},
     doi = {10.5802/crmath.637},
     zbl = {07945473},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/crmath.637/}
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Qiao, Huijie; Zhu, Shengqing. A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems. Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1287-1299. doi: 10.5802/crmath.637

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