The stationarity of multidimensional generalized Ornstein-Uhlenbeck processes

The multidimensional generalized Ornstein-Uhlenbeck process is defined as an extended version of the generalized Ornstein-Uhlenbeck process of which integral is with respect to a multidimensional Lévy process. The condition for the stationarity of the process and that for the convergence are respectively studied. The relationship between these two conditions is also clarified.