On the Stability of Kalman--Bucy Diffusion Processes
| hal.structure.identifier | Commonwealth Scientific and Industrial Research Organisation [Australia] [CSIRO] | |
| dc.contributor.author | BISHOP, Adrian | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| dc.date.accessioned | 2024-04-04T03:07:16Z | |
| dc.date.available | 2024-04-04T03:07:16Z | |
| dc.date.issued | 2017-11-02 | |
| dc.identifier.issn | 0363-0129 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193421 | |
| dc.description.abstractEn | The Kalman--Bucy filter is the optimal state estimator for an Ornstein--Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional exact implementation of the optimal Bayes filter. It is generally the only such finite-dimensional exact instance of the Bayes filter for continuous state-space models. Consequently, this filter has been studied extensively in the literature since the seminal 1961 paper of Kalman and Bucy. The purpose of this work is to review, re-prove and refine existing results concerning the dynamical properties of the Kalman--Bucy filter so far as they pertain to filter stability and convergence. The associated differential matrix Riccati equation is a focal point of this study with a number of bounds, convergence, and eigenvalue inequalities rigorously proven. New results are also given in the form of exponential and comparison inequalities for both the filter and the Riccati flow. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.title.en | On the Stability of Kalman--Bucy Diffusion Processes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1137/16M1102707 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1610.04686 | |
| bordeaux.journal | SIAM Journal on Control and Optimization | |
| bordeaux.page | 4015 - 4047 | |
| bordeaux.volume | 55 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 6 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01669244 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01669244v1 | |
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