Some properties of exponential integrals of Lévy processes and examples
| dc.creator | Kondo, Hitoshi | |
| dc.creator | Maejima, Makoto | |
| dc.creator | Sato, Ken-iti | |
| dc.date | 2006-06-04 | |
| dc.date.accessioned | 2026-07-07T07:14:46Z | |
| dc.date.available | 2026-07-07T07:14:46Z | |
| dc.description | The improper stochastic integral $Z=\int_0^{\infty-}\exp(-X_{s-})dY_s$ is studied, where $\{(X_t, Y_t), t \geqslant 0 \}$ is a Lévy process on $\mathbb R ^{1+d}$ with $\{X_t \}$ and $\{Y_t \}$ being $\mathbb R$-valued and $\mathbb R ^d$-valued, respectively. The condition for existence and finiteness of $Z$ is given and then the law $\mathcal L(Z)$ of $Z$ is considered. Some sufficient conditions for $\mathcal L(Z)$ to be selfdecomposable and some sufficient conditions for $\mathcal L(Z)$ to be non-selfdecomposable but semi-selfdecomposable are given. Attention is paid to the case where $d=1$, $\{X_t\}$ is a Poisson process, and $\{X_t\}$ and $\{Y_t\}$ are independent. An example of $Z$ of type $G$ with selfdecomposable mixing distribution is given. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606084 | |
| dc.identifier | http://arxiv.org/abs/math/0606084 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113018 | |
| dc.subject | Probability | |
| dc.subject | 60E07, 60G51, 60H05 | |
| dc.title | Some properties of exponential integrals of Lévy processes and examples | |
| dc.type | text |