@article{ECP1232,
author = {Hitoshi Kondo and Makoto Maejima and Ken-iti Sato},
title = {Some properties of exponential integrals of Levy processes and examples},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {11},
year = {2006},
keywords = {Generalized Ornstein-Uhlenbeck process, L'evy process, selfdecomposability, semi-selfdecomposability, stochastic integral},
abstract = {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},
pages = {no. 30, 291-303},
issn = {1083-589X},
doi = {10.1214/ECP.v11-1232},
url = {http://ecp.ejpecp.org/article/view/1232}}