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On the stability and the uniform propagation of chaos properties of Ensemble Kalman-Bucy filters
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| dc.contributor.author | DEL MORAL, Pierre | |
| hal.structure.identifier | Départment d'Informatique Appliquée [Saint Etienne] | |
| dc.contributor.author | TUGAUT, Julian | |
| dc.date.accessioned | 2024-04-04T03:08:43Z | |
| dc.date.available | 2024-04-04T03:08:43Z | |
| dc.date.issued | 2016-10-03 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193549 | |
| dc.description.abstractEn | The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov type particle interpretation of the Kalman-Bucy diffusions. In contrast to more conventional particle filters and nonlinear Markov processes these models are designed in terms of a diffusion process with a diffusion matrix that depends on particle covariance matrices. Besides some recent advances on the stability of nonlinear Langevin type diffusions with drift interactions, the long-time behavior of models with interacting diffusion matrices and conditional distribution interaction functions has never been discussed in the literature. One of the main contributions of the article is to initiate the study of this new class of models The article presents a series of new functional inequalities to quantify the stability of these nonlinear diffusion processes. In the same vein, despite some recent contributions on the convergence of the Ensemble Kalman filter when the number of sample tends to infinity very little is known on stability and the long-time behaviour of these mean-field interacting type particle filters. The second contribution of this article is to provide uniform propagation of chaos properties as well as L n-mean error estimates w.r.t. to the time horizon. Our regularity condition is also shown to be sufficient and necessary for the uniform convergence of the Ensemble Kalman filter. The stochastic analysis developed in this article is based on an original combination of functional inequalities and Foster-Lyapunov techniques with coupling, martingale techniques, random matrices and spectral analysis theory. | |
| dc.language.iso | en | |
| dc.subject.en | interacting particle systems | |
| dc.subject.en | nonlinear Markov processes | |
| dc.subject.en | random covariance matrices | |
| dc.subject.en | Ensemble Kalman Filter | |
| dc.subject.en | Kalman-Bucy filter | |
| dc.subject.en | Riccati equations | |
| dc.subject.en | ill-conditioned systems | |
| dc.subject.en | Mean-field particle models | |
| dc.subject.en | Sequential Monte Carlo methods | |
| dc.title.en | On the stability and the uniform propagation of chaos properties of Ensemble Kalman-Bucy filters | |
| dc.type | Rapport | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1605.09329 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.type.institution | Arxiv | |
| bordeaux.type.report | rr | |
| hal.identifier | hal-01593877 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01593877v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2016-10-03&rft.au=DEL%20MORAL,%20Pierre&TUGAUT,%20Julian&rft.genre=unknown |
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