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Some properties of exponential integrals of Levy processes and examples

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1.	Title	Title of document	Some properties of exponential integrals of Levy processes and examples
2.	Creator	Author's name, affiliation, country	Hitoshi Kondo; Department of Mathematics, Keio University
2.	Creator	Author's name, affiliation, country	Makoto Maejima; Department of Mathematics, Keio University
2.	Creator	Author's name, affiliation, country	Ken-iti Sato; No affiliation
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Generalized Ornstein-Uhlenbeck process, L'evy process, selfdecomposability, semi-selfdecomposability, stochastic integral
3.	Subject	Subject classification	60E07, 60G51, 60H05
4.	Description	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
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2006-12-04
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1232
10.	Identifier	Digital Object Identifier	10.1214/ECP.v11-1232
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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