Tail of a linear diffusion with Markov switching
Résumé
Let Y be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X, i.e. dYt=a(Xt)Ytdt+σ(Xt)dWt, Y0=y0. Ergodicity conditions for Y have been obtained. Here we investigate the tail property of the stationary distribution of this model. A characterization of the only two possible cases is established: light tail or polynomial tail. Our method is based on discretizations and renewal theory.