Kalman filter and quantization (Q5919905)

The filtration of diffusion processes is closely related to classical and quantum mechanics provided the linear and nonlinear filtration problem is associated with a classical Hamiltonian system for which the quantization lead us to the original filtration. The author provides a heuristic justification for a similarity table of the two methods connecting Schrödinger equation, Feynman integrals and Heisenberg equations with the corresponding Zakai equation, Girsanov formula and Kalman-Bucy filter.