Feynman Path Integral Discretization And Its Applications to Nonlinear Filtering

摘要

In continuous nonlinear filtering theory, we are interested in solving certain parabolic second-order partial differential equations (PDEs), such as the Fokker-Planck equation. The fundamental solution of such PDEs can be written in various ways, such as the Feynman-Kac integral and the Feynman path integral (FPI). In addition, the FPI can be defined in several ways. In this paper, the FPI definition based on discretization is reviewed. This has the advantage of being rigorously defined as limits of finite-dimensional integrals. The rigorous and non-rigorous approaches are compared in terms of insight and successes in nonlinear filtering as well as other areas in mathematics.