 |
 |
|
|
| HAL: hal-00441645, version 1 |
| arXiv: 0912.3231 |
| Detailed view |  Export this paper |
 |
| Available versions: | v1 (2009-12-17) | v2 (2009-12-17) |
|
|
|
|
| Long time behavior of diffusions with Markov switching |
|
|
| Jean-Baptiste Bardet 1, 2Hélène Guerin 1 |
|
|
| (2009-12-16) |
|
|
|
| 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: | Institut de Recherche Mathématique de Rennes (IRMAR) |
|
|
|
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
|
|
| 2: | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
|
|
|
CNRS : UMR6085 – Université de Rouen |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Probability |
|
|
| Ornstein–Uhlenbeck diffusion – Markov switching – jump process – random difference equation – light tail – heavy tail – Laplace transform |
|
|
|
| Attached file list to this document: | ||||||||||
|
||||||||||
|
|
|
| hal-00441645, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00441645 | |
| oai:hal.archives-ouvertes.fr:hal-00441645 | |
| From: Hélène Guérin | |
| Submitted on: Wednesday, 16 December 2009 22:48:36 | |
| Updated on: Thursday, 17 December 2009 09:56:08 | |
