 |
|
|
|
| HAL : hal-00426415, version 1 |
| arXiv : 0910.4870 |
| Fiche détaillée |  Récupérer au format |
|
|
|
|
| Stability of Feynman-Kac formulae with path-dependent potentials |
|
|
| Nicolas Chopin 1, 2Pierre Del Moral 3 |
|
|
| (2009) |
|
|
|
| Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but other models and algorithms of practical interest fall in this category. We study the asymptotic stability of such particle algorithms as time goes to infinity. As a corollary, practical conditions for the stability of the mixture Kalman filter, and a mixture GARCH filter, are derived. Finally, we show that our results can also lead to weaker conditions for the stability of standard particle algorithms, such that the potential function depends on the last state only. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Centre de Recherche en Économie et Statistique (CREST) |
|
|
|
INSEE – École Nationale de la Statistique et de l'Administration Économique |
|
|
| 2 : | École Nationale de la Statistique et de l'Administration Économique (ENSAE) |
|
|
|
ENSAE ParisTech |
|
|
| 3 : | ALEA (INRIA Bordeaux - Sud-Ouest) |
|
|
|
INRIA – Université de Bordeaux – CNRS : UMR5251 |
|
|
| 4 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
|
|
|
CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie |
|
|
| Feynman-Kac formulae – mixture Kalman filter – path-dependent potential function – Particle filter |
|
|
|
|
|
| hal-00426415, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00426415 | |
| oai:hal.archives-ouvertes.fr:hal-00426415 | |
| Contributeur : Nicolas Chopin | |
| Soumis le : Lundi 26 Octobre 2009, 11:45:49 | |
| Dernière modification le : Lundi 26 Octobre 2009, 14:07:04 | |
