On the absolute continuity of multidimensional Ornstein-Uhlenbeck processes (Q644787)

Let \(X_t\) be a \(d\)-dimensional Lévy-Ornstein-Uhlenbeck process without Gaussian part and with non-singular matrix drift coefficient \(A\). It is shown that the law of \(X_t\) is absolutely continuous if and only if the jump measure of the underlying Lévy process satisfies a geometric exhaustion condition with respect to \(A\). In that case the underlying Lévy process itself may be singular or even have a one-dimensional discrete jump measure.