Tail of a linear diffusion with Markov switching

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 + σ(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. © Institute of Mathematical Statistics, 2005.published_or_final_versio