Strong Feller property and ergodicity of generalized OU processes

By a coupling method, we give some upper bound estimates for the variations of the transition probabilities of a generalized Ornstein-Uhlenbeck process driven by two independent Lévy processes. From these results, we derive the strong Feller 性质 and the exponential ergodicity of the process in Wasserstein distances under 条件 given directly by the characteristic triplets of the driving noises.