A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems

Huijie Qiao; Shengqing Zhu

doi:10.5802/crmath.637

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]

Huijie Qiao ¹ ; Shengqing Zhu ¹

¹ School of Mathematics, Southeast University, Nanjing, Jiangsu 211189, P.R.China

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1287-1299.

Résumé
Abstract

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 $L^{2}$ .

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.

Reçu le : 2023-11-26
Accepté le : 2024-03-31
Publié le : 2024-11-14

DOI : 10.5802/crmath.637

Classification : 60G35
Mots clés : Multiscale McKean–Vlasov stochastic systems, average principle, nonlinear filtering, limit theorem

Affiliations des auteurs :

Huijie Qiao ¹ ; Shengqing Zhu 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 = {Huijie Qiao and Shengqing Zhu},
     title = {A limit theorem of nonlinear filtering for multiscale {McKean{\textendash}Vlasov} stochastic systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1287--1299},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.637},
     language = {en},
}

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Huijie Qiao; Shengqing Zhu. A limit theorem of nonlinear filtering for multiscale McKean–Vlasov stochastic systems. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1287-1299. doi : 10.5802/crmath.637. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.637/

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