Euclidean Quantum Mechanics and Universal Nonlinear Filtering

Entropy

关键词: Bayesian filtering and estimation;    Fokker-Planck Equation;    Kolmogorov Equation;    stochastic differential equations;    Duncan-Mortensen-Zakai (DMZ) Equation;    nonlinear filtering;    Feynman path integral;   

DOI  :  10.3390/e11010042

来源: mdpi

【 摘 要 】

An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr¨odinger equation.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.