On the Linear-Exponential Filtering Problem for General Gaussian Processes
| Autor: | A. Le Breton, M. Viot, Marina Kleptsyna |
|---|---|
| Přispěvatelé: | Département de Mathématiques [Le Mans], Le Mans Université (UM), Statistique et Modélisation Stochatisque (SMS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2009 |
| Předmět: |
0209 industrial biotechnology
Control and Optimization Markov process 02 engineering and technology Conditional expectation 01 natural sciences 010104 statistics & probability symbols.namesake 020901 industrial engineering & automation Quadratic equation [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Riccati equation Filtering problem Applied mathematics 0101 mathematics Gaussian process Mathematics Discrete mathematics Stochastic process Applied Mathematics optimal filtering Mathematical analysis [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Conditional probability distribution Filter (signal processing) Exponential function risk-sensitive filtering filtering error MSC: 60G15 60G44 62M20 symbols exponential criteria Conditional variance Riccati-Volterra equation |
| Zdroj: | CDC CDC 2009-48th IEEE Conference on Decision and Control CDC 2009-48th IEEE Conference on Decision and Control, Dec 2009, Shanghai, China. pp.2646-2651, ⟨10.1109/CDC.2009.5400249⟩ SIAM Journal on Control and Optimization SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2008, 47 (6), pp.2886-2911. ⟨10.1137/070705908⟩ |
| ISSN: | 1095-7138 0363-0129 |
| DOI: | 10.1137/070705908 |
| Popis: | International audience; The explicit solution of the filtering problem with exponential criteria for a general Gaussian signal is obtained through an approach which is based on a conditional Cameron-Martin-type formula. This key formula is derived for conditional expectations of exponentials of some quadratic functionals of a general continuous Gaussian process. The formula involves conditional expectations and conditional covariances in some auxiliary optimal risk-neutral filtering problem which is used in the proof. Closed form equations of the Itô-Volterra- and Riccati-Volterra-types for these ingredients are provided. Particular cases for which the results can be further elaborated are investigated. |
| Databáze: | OpenAIRE |
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