The Applications of Yau-Yau Algorithm on McKean-Vlasov Filtering Problem Dedicated to Professor Peter Caines on the occasion of his 80th Birthday  

作　　者：SUN Zeju YAU Stephen Shing-Toung 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China [2]Beijing Institute of Mathematical Sciences and Applications(BIMSA),Beijing 101408,China

出　　处：《Journal of Systems Science & Complexity》2025年第1期79-97,共19页系统科学与复杂性学报(英文版)

基　　金：supported by the National Natural Science Foundation of China under Grant No.123B2020;by Tsinghua University Education Foundation fund under Grant No.042202008.

摘　　要：The McKean-Vlasov filtering problem is a special kind of filtering problem,with the state and/or observation processes governed by McKean-Vlasov stochastic differential equations,which has extensive applications in various scenarios.In this paper,the authors will propose a novel numerical algorithm to solve the McKean-Vlasov filtering problem based on the Hermite spectral method under the framework of Yau-Yau algorithm.As the first approach to numerically solving the Duncan-Mortensen-Zakai equation associated with the McKean-Vlasov filtering problem,the proposed algorithm can provide accurate estimations of the conditional expectation and conditional probability density of the state process with a reasonable online computational complexity.The efficiency of the proposed algorithm is verified both theoretically and numerically in this paper.

关 键 词：Duncan-Mortensen-Zakai equation Hermite spectral method McKean-Vlasov equation Nonlinear filtering Yau-Yau algorithm 

分 类 号：O211[理学—概率论与数理统计]