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 - <p style="text-align: justify;">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.</p>