Tail of a linear diffusion with Markov switching

Beno�te de Saporta, Jian-Feng Yao
2005 The Annals of Applied Probability  
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.
doi:10.1214/105051604000000828 fatcat:2xyxfjg7wzhkza3z3uupql4on4