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-P...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.展开更多
基金supported by the U.S.National Science Foundation through Project DMS-2142672by the U.S.Department of Energy,Office of Science,Office of Advanced Scientific Computing Research,Applied Mathematics Program under Grant DE-SC0022297.
文摘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.
