  Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic
Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. Ergodicity
conditions for Y have been obtained. Here we investigate the tail propriety of
the stationary distribution of this model. A characterization of either heavy
or light tail case is established. The method is based on a renewal theorem for
systems of equations with distributions on R.
