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

Euclidean Quantum Mechanics and Universal Nonlinear Filtering

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Received: 1 January 2009; Accepted: 6 February 2009 / Published: 12 February 2009
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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MDPI and ACS Style

Balaji, B. Euclidean Quantum Mechanics and Universal Nonlinear Filtering. Entropy 2009, 11, 42-58.

AMA Style

Balaji B. Euclidean Quantum Mechanics and Universal Nonlinear Filtering. Entropy. 2009; 11(1):42-58.

Chicago/Turabian Style

Balaji, Bhashyam. 2009. "Euclidean Quantum Mechanics and Universal Nonlinear Filtering." Entropy 11, no. 1: 42-58.


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