Euclidean Quantum Mechanics and Universal Nonlinear Filtering
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 co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2009-02-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/11/1/42/ |
| _version_ | 1798042048327057408 |
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| author | Bhashyam Balaji |
| author_facet | Bhashyam Balaji |
| author_sort | Bhashyam Balaji |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:30:02Z |
| format | Article |
| id | doaj.art-31890d822b7340b3b8d57740018a8dff |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:30:02Z |
| publishDate | 2009-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-31890d822b7340b3b8d57740018a8dff2022-12-22T03:59:31ZengMDPI AGEntropy1099-43002009-02-01111425810.3390/e11010042Euclidean Quantum Mechanics and Universal Nonlinear FilteringBhashyam BalajiAn 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.http://www.mdpi.com/1099-4300/11/1/42/Bayesian filtering and estimationFokker-Planck EquationKolmogorov Equationstochastic differential equationsDuncan-Mortensen-Zakai (DMZ) Equationnonlinear filteringFeynman path integral |
| spellingShingle | Bhashyam Balaji Euclidean Quantum Mechanics and Universal Nonlinear Filtering Entropy Bayesian filtering and estimation Fokker-Planck Equation Kolmogorov Equation stochastic differential equations Duncan-Mortensen-Zakai (DMZ) Equation nonlinear filtering Feynman path integral |
| title | Euclidean Quantum Mechanics and Universal Nonlinear Filtering |
| title_full | Euclidean Quantum Mechanics and Universal Nonlinear Filtering |
| title_fullStr | Euclidean Quantum Mechanics and Universal Nonlinear Filtering |
| title_full_unstemmed | Euclidean Quantum Mechanics and Universal Nonlinear Filtering |
| title_short | Euclidean Quantum Mechanics and Universal Nonlinear Filtering |
| title_sort | euclidean quantum mechanics and universal nonlinear filtering |
| topic | Bayesian filtering and estimation Fokker-Planck Equation Kolmogorov Equation stochastic differential equations Duncan-Mortensen-Zakai (DMZ) Equation nonlinear filtering Feynman path integral |
| url | http://www.mdpi.com/1099-4300/11/1/42/ |
| work_keys_str_mv | AT bhashyambalaji euclideanquantummechanicsanduniversalnonlinearfiltering |