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 Electronic Communications in Probability > Vol. 11 (2006) > Paper 30 open journal systems 


Some properties of exponential integrals of Levy processes and examples

Hitoshi Kondo, Department of Mathematics, Keio University
Makoto Maejima, Department of Mathematics, Keio University
Ken-iti Sato,


Abstract
The improper stochastic integral $Z=int_0^{infty-}exp(-X_{s-})dY_s$ is studied, where ${ (X_t ,Y_t) , t ges 0 }$ 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 $law(Z)$ of $Z$ is considered. Some sufficient conditions for $law(Z)$ to be selfdecomposable and some sufficient conditions for $law(Z)$ 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


Full text: PDF

Pages: 291-303

Published on: December 4, 2006
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Electronic Communications in Probability. ISSN: 1083-589X