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Convergence analysis of kernel learning FBSDE filter

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  • Yunzheng Lyu
  • Feng Bao

Abstract

Kernel learning forward backward SDE 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 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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  • Yunzheng Lyu & Feng Bao, 2024. "Convergence analysis of kernel learning FBSDE filter," Papers 2405.13390, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2405.13390
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    File URL: http://arxiv.org/pdf/2405.13390
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