A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise
A Bayes-type formula is derived for the nonlinear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well-known Kallianpur-Striebel formula in the classical non-linear filter setting. We also dis...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/259091 |
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| author | Vidyadhar Mandrekar Thilo Meyer-Brandis Frank Proske |
| author_facet | Vidyadhar Mandrekar Thilo Meyer-Brandis Frank Proske |
| author_sort | Vidyadhar Mandrekar |
| collection | DOAJ |
| description | A Bayes-type formula is derived for the nonlinear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well-known Kallianpur-Striebel formula in the classical non-linear filter setting. We also discuss Zakai-type equations for both the unnormalized conditional distribution as well as unnormalized conditional density in case the signal is a Markovian jump diffusion. |
| format | Article |
| id | doaj-art-42136b69f1bf4c769f1b7ef898b0681a |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-42136b69f1bf4c769f1b7ef898b0681a2025-02-03T05:58:37ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/259091259091A Bayes Formula for Nonlinear Filtering with Gaussian and Cox NoiseVidyadhar Mandrekar0Thilo Meyer-Brandis1Frank Proske2Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USADepartment of Mathematics, University of Munich, Theresienstrasse 39, 80333 Munich, GermanyCenter of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, NorwayA Bayes-type formula is derived for the nonlinear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well-known Kallianpur-Striebel formula in the classical non-linear filter setting. We also discuss Zakai-type equations for both the unnormalized conditional distribution as well as unnormalized conditional density in case the signal is a Markovian jump diffusion.http://dx.doi.org/10.1155/2011/259091 |
| spellingShingle | Vidyadhar Mandrekar Thilo Meyer-Brandis Frank Proske A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise Journal of Probability and Statistics |
| title | A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise |
| title_full | A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise |
| title_fullStr | A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise |
| title_full_unstemmed | A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise |
| title_short | A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise |
| title_sort | bayes formula for nonlinear filtering with gaussian and cox noise |
| url | http://dx.doi.org/10.1155/2011/259091 |
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