The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Exact finite-dimensional filters for certain diffusions with nonlinear drift
Abstract
Let and be independent Wiener processes, and consider the task of estimating a diffusion solving the stochastic DE dx t =f(x t )dt+dw t on the basis of noisy observations defined bydy t =x t dt+db t . This problem is governed by the filtering equation for the unnormalized conditional density with A * the forwarded operator Theorem: if then the fundamental solution of the filtering equation can be written explicity in terms of a small number of statistics satisfying a matrixvector equation. The Lie algebraic interpretation of this result is studied and described. Extensions to many dimensions and applications to optimal stochastic control readily follow.
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Citations
Cites
On the optimal filtering of diffusion processes
Zakai, M. (1969) · Probability Theory and Related Fields · doi:10.1007/bf00536382 · Cited by 693
Some Applications of Stochastic Differential Equations to Optimal Nonlinear Filtering
Wonham, W. M. (1964) · Journal of the Society for Industrial and Applied Mathematics Series A Control · doi:10.1137/0302028 · Cited by 423
Cited by
Arasaratnam, I., & Haykin, S. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2019800 · Cited by 3,380
Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulations
Arasaratnam, I., Haykin, S., & Hurd, T. R. (2010) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2010.2056923 · Cited by 580
On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems
Sarkka, S. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.904453 · Cited by 553
Applied Stochastic Differential Equations
Särkkä, S., & Solin, A. (2019) · doi:10.1017/9781108186735 · Cited by 326
Wide-Sense Estimation on the Special Orthogonal Group
Chiuso, A., Picci, G., & Soatto, S. (2008) · Communications in Information and Systems · doi:10.4310/cis.2008.v8.n3.a1 · Cited by 25
Metadata
- Authors
- BeneŠ, V. E.
- Venue
- Stochastics
- Publisher
- Informa UK Limited
- Published
- 1981-06
- Volume
- 5
- Issue
- 1-2
- Pages
- 65-92
- ISSN
- 0090-9491 (ISSN-L)
- OpenAlex
- W2073283839
- Cited by
- 416
- References
- 2
- FWCI
- 20.83
- Type
- journal article
- Language
- en
- Open access
- closed
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- BeneŠ, V. E. (1981). Exact finite-dimensional filters for certain diffusions with nonlinear drift. Stochastics. https://doi.org/10.1080/17442508108833174
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