Convergence Analysis of Kernel Learning FBSDE Filter

Convergence Analysis of Kernel Learning FBSDE Filter

Year:    2024

Author:    Yunzheng Lyu, Feng Bao

Communications in Mathematical Research , Vol. 40 (2024), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2024-0017

Communications in Mathematical Research , Vol. 40 (2024), Iss. 3 : pp. 313–342

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

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

Author Details

Yunzheng Lyu

Feng Bao