 |
|
|
|
| HAL : hal-00441645, version 2 |
| arXiv : 0912.3231 |
| Fiche détaillée |  Récupérer au format |
|
|
| ALEA : Latin American Journal of Probability and Mathematical Statistics 7 (2010) 151-170 |
|
|
| Versions disponibles : | v1 (17-12-2009) | v2 (17-12-2009) |
|
|
|
|
| Long time behavior of diffusions with Markov switching |
|
|
| Jean-Baptiste Bardet 1Hélène Guérin 2 |
|
|
| (2010) |
|
|
|
| Let $Y$ be an Ornstein-Uhlenbeck diffusion governed by an ergodic finite state Markov process $X$: $dY_t=-\lambda(X_t)Y_tdt+\sigma(X_t)dB_t$, $Y_0$ given. Under ergodicity condition, we get quantitative estimates for the long time behavior of $Y$. We also establish a trichotomy for the tail of the stationary distribution of $Y$: it can be heavy (only some moments are finite), exponential-like (only some exponential moments are finite) or Gaussian-like (its Laplace transform is bounded below and above by Gaussian ones). The critical moments are characterized by the parameters of the model. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
|
|
|
CNRS : UMR6085 – Université de Rouen |
|
|
| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
|
|
|
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
|
|
|
|
|
|
|
|
|
| Théorie ergodique ; Processus stochastiques |
|
|
|
|
| Domaine | : | Mathématiques/Probabilités |
|
|
| Ornstein–Uhlenbeck diffusion – Markov switching – jump process – random difference equation – light tail – heavy tail – Laplace transform |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00441645, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00441645 | |
| oai:hal.archives-ouvertes.fr:hal-00441645 | |
| Contributeur : Hélène Guérin | |
| Soumis le : Jeudi 17 Décembre 2009, 18:22:03 | |
| Dernière modification le : Lundi 5 Juillet 2010, 09:23:50 | |
