| Título: | Some properties of exponential integrals of Levy processes and examples |
| Autores: |
Kondo, Hitoshi; Department of Mathematics, Keio University Maejima, Makoto; Department of Mathematics, Keio University Sato, Ken-iti; No affiliation |
| Fecha: | 2006-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Generalized Ornstein-Uhlenbeck process, L'evy process, selfdecomposability, semi-selfdecomposability, stochastic integral 60E07, 60G51, 60H05 |
| Descripción: | The improper stochastic integral $Z= \int_0^{\infty-}\exp(-X_{s-})dY_s$ is studied, where ${ (X_t ,Y_t) , t \geq 0 }$ is a L'evy process on $R ^{1+d}$ with ${X_t }$ and ${Y_t }$ being $R$-valued and $R ^d$-valued, respectively. The condition for existence and finiteness of $Z$ is given and then the law ${\cal L}(Z)$ of $Z$ is considered. Some sufficient conditions for ${\cal L}(Z)$ to be selfdecomposable and some sufficient conditions for ${\cal L}(Z)$ 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 |
| Idioma: | No aplica |
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