On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process

Abstract

We prove the following probabilistic properties of a multidimensional Ornstein-Uhlenbeck process driven by a general Lévy process, under mild regularity conditions: the strong Feller property; the existence of a smooth transition density; and the exponential β-mixing property. As a class of possible invariant distributions of an Ornstein-Uhlenbeck process, we also discuss centred and non-skewed multidimensional generalized hyperbolic distributions.