Tail of a linear diffusion with Markov switching

Benoîte de Saporta (1) , Jian-Feng Yao (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 VISTA - Vision spatio-temporelle et active

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.

Domaines: Probabilités [math.PR]

Benoîte de Saporta, Jian-Feng Yao. Tail of a linear diffusion with Markov switching. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 339 (9), pp.643-646. ⟨hal-00274880⟩