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Entropy 2009, 11(1), 42-58; doi:10.3390/e11010042
Article

Euclidean Quantum Mechanics and Universal Nonlinear Filtering

Received: 1 January 2009 / Accepted: 6 February 2009 / Published: 12 February 2009
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Abstract

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.
Keywords: Bayesian filtering and estimation; Fokker-Planck Equation; Kolmogorov Equation; stochastic differential equations; Duncan-Mortensen-Zakai (DMZ) Equation; nonlinear filtering; Feynman path integral Bayesian filtering and estimation; Fokker-Planck Equation; Kolmogorov Equation; stochastic differential equations; Duncan-Mortensen-Zakai (DMZ) Equation; nonlinear filtering; Feynman path integral
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Balaji, B. Euclidean Quantum Mechanics and Universal Nonlinear Filtering. Entropy 2009, 11, 42-58.

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