Some properties of exponential integrals of Lévy processes and examples

Hitoshi Kondo, Makoto Maejima, Ken-iti Sato

The improper stochastic integral $Z={\int }_0^{\infty -}\exp (-X_{s-})d{Y}_s$ is studied, where $\{(X_t,Y_t),t⩾0\}$ is a Lévy process on ${\mathbb{R}}^{1+d}$ with $\{X_t\}$ an…