Convergence Analysis of Kernel Learning FBSDE Filter

Authors

  • Yunzheng Lyu
  • Feng Bao

DOI:

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

Keywords:

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

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.

Published

2024-09-09

Issue

Section

Articles