Convergence Analysis of Kernel Learning FBSDE Filter (Communications in Mathematical Research, 2024)
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, andemploys kernel density estimation (KDE) to approximate density. This algorithm has shown more superior performance than mainstream particle filtermethod, in both convergence speed and efficiency of solving high dimensionproblems. However, this method has only been shown to converge empirically.In this paper, we present a rigorous analysis to demonstrate its local and globalconvergence, and provide theoretical support for its empirical results.