 |
 |
|
|
| HAL: hal-00441640, version 2 |
| arXiv: 0912.3232 |
| Detailed view |  Export this paper |
 |
| Available versions: | v1 (2009-12-16) | v2 (2009-12-23) |
|
|
|
|
| On the Laplace transform of perpetuities with thin tails |
|
|
| Jean-Baptiste Bardet 1Hélène Guérin 2 |
|
|
| (2009-12-16) |
|
|
|
| We consider the random variables $R$ which are solutions of the distributional equation $R\overset{\cL}{=}MR+Q$, where $(Q,M)$ is independent of $R$ and $\ABS{M}\leq 1$. Goldie and Grübel showed that the tails of $R$ are no heavier than exponential. In this note we provide the exact lower and upper bounds of the domain of the Laplace transform of $R$. |
|
|
|
|
|
|
|
|
|
|
|
| 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 – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Probability |
|
|
| Perpetuity – Stochastic difference equation – Laplace transform – tail behavior |
|
|
|
| Attached file list to this document: | ||||||||||
|
||||||||||
|
|
|
| hal-00441640, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00441640 | |
| oai:hal.archives-ouvertes.fr:hal-00441640 | |
| From: Hélène Guérin | |
| Submitted on: Wednesday, 23 December 2009 08:06:53 | |
| Updated on: Tuesday, 23 March 2010 14:33:49 | |
