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Volume 40, Issue 3
Convergence Analysis of Kernel Learning FBSDE Filter

Yunzheng Lyu & Feng Bao

DOI: 10.4208/cmr.2024-0017

Commun. Math. Res., 40 (2024), pp. 313-342.

Published online: 2024-09

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  • Abstract

Kernel learning forward backward stochastic differential equations (FBSDE) filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. It builds from forward backward SDE for Fokker-Planker equation, which defines evolving density for the state variable, and employs kernel density estimation (KDE) to approximate density. This algorithm has shown more superior performance than mainstream particle filter method, in both convergence speed and efficiency of solving high dimension problems. However, this method has only been shown to converge empirically. In this paper, we present a rigorous analysis to demonstrate its local and global convergence, and provide theoretical support for its empirical results.

  • Keywords

Forward backward stochastic differential equations, kernel density estimation, nonlinear filtering problems, convergence analysis.

  • AMS Subject Headings

93E11, 65B99, 65C05, 65C35, 65C60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-313, author = {Lyu , Yunzheng and Bao , Feng}, title = {Convergence Analysis of Kernel Learning FBSDE Filter}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {3}, pages = {313--342}, abstract = {

Kernel learning forward backward stochastic differential equations (FBSDE) filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. It builds from forward backward SDE for Fokker-Planker equation, which defines evolving density for the state variable, and employs kernel density estimation (KDE) to approximate density. This algorithm has shown more superior performance than mainstream particle filter method, in both convergence speed and efficiency of solving high dimension problems. However, this method has only been shown to converge empirically. In this paper, we present a rigorous analysis to demonstrate its local and global convergence, and provide theoretical support for its empirical results.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2024-0017}, url = {http://global-sci.org/intro/article_detail/cmr/23414.html} }
TY - JOUR T1 - Convergence Analysis of Kernel Learning FBSDE Filter AU - Lyu , Yunzheng AU - Bao , Feng JO - Communications in Mathematical Research VL - 3 SP - 313 EP - 342 PY - 2024 DA - 2024/09 SN - 40 DO - http://doi.org/10.4208/cmr.2024-0017 UR - https://global-sci.org/intro/article_detail/cmr/23414.html KW - Forward backward stochastic differential equations, kernel density estimation, nonlinear filtering problems, convergence analysis. AB -

Kernel learning forward backward stochastic differential equations (FBSDE) filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. It builds from forward backward SDE for Fokker-Planker equation, which defines evolving density for the state variable, and employs kernel density estimation (KDE) to approximate density. This algorithm has shown more superior performance than mainstream particle filter method, in both convergence speed and efficiency of solving high dimension problems. However, this method has only been shown to converge empirically. In this paper, we present a rigorous analysis to demonstrate its local and global convergence, and provide theoretical support for its empirical results.

Lyu , Yunzheng and Bao , Feng. (2024). Convergence Analysis of Kernel Learning FBSDE Filter. Communications in Mathematical Research . 40 (3). 313-342. doi:10.4208/cmr.2024-0017
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