Nonlinear filtering algorithms based on averaging over characteristics and on the innovation approach
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About this item
| Description: |
Tretyakov, M (University of Leicester)
Monday 14 June 2010, 14:50-15:40 |
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| Created: | 2010-06-16 12:00 | ||
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| Collection: | Stochastic Partial Differential Equations | ||
| Publisher: | Isaac Newton Institute | ||
| Copyright: | Tretyakov, M | ||
| Language: | eng (English) | ||
| Distribution: |
World
(downloadable)
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| Credits: |
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| Explicit content: | No | ||
| Aspect Ratio: | 4:3 | ||
| Screencast: | No | ||
| Bumper: | /sms-ingest/static/new-4x3-bumper.dv | ||
| Trailer: | /sms-ingest/static/new-4x3-trailer.dv | ||
| Abstract: | It is well known that numerical methods for nonlinear filtering problems, which directly use the Kallianpur-Striebel formula, can exhibit computational instabilities due to the presence of very large or very small exponents in both the numerator and denominator of the formula. We obtain computationally stable schemes by exploiting the innovation approach. We propose Monte Carlo algorithms based on the method of characteristics for linear parabolic stochastic partial differential equations. Convergence and some properties of the considered algorithms are studied. Variance reduction techniques are discussed. Results of some numerical experiments are presented. The talk is based on a joint work with G.N. Milstein. |
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