Convergence Analysis of Kernel Learning FBSDE Filter  

作　　者：Yunzheng Lyu Feng Bao 

机构地区：[1]Department of Mathematics,Florida State University,FL 32306,USA

出　　处：《Communications in Mathematical Research》2024年第3期313-342,共30页数学研究通讯（英文版）

基　　金：supported by the U.S.National Science Foundation through Project DMS-2142672;by the U.S.Department of Energy,Office of Science,Office of Advanced Scientific Computing Research,Applied Mathematics Program under Grant DE-SC0022297.

摘　　要：Kernel learning forward backward stochastic differential equations(FBSDE)filter is an iterative and adaptive meshfree approach to solve the non-linear 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 algo-rithm 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.

关 键 词：Forward backward stochastic differential equations kernel density estima-tion nonlinear filtering problems convergence analysis. 

分 类 号：O175[理学—数学]