Continuity properties and infinite divisibility of stationary distributions of some generalized Ornstein--Uhlenbeck processes

Alexander Lindner, Ken-iti Sato

Properties of the law $\mu$ of the integral ${\int }_0^{\infty }{c}^{-N_{t-}}d{Y}_t$ are studied, where $c>1$ and $\{(N_t,Y_t),t\ge 0\}$ is a bivariate Lévy process such that $\{N_t\}$ and…