Tail of a linear diffusion with Markov switching (Q5916118)

This paper deals with an Ornstein-Uhlenbeck diffusion \(Y\) governed by a stationary and ergodic Markov jump process \(X\), i.e. \(dY_t=a(X_t)Y_tdt+\sigma(X_t)\,dW_t\), \(Y_0=y_0\). Ergodicity conditions for \(Y\) have been obtained. They also investigate the tail property of the stationary distribution of this model. A characterisation of the only two possible cases is established: light tail or polynomial tail. The method of investigation is based on discretizations and renewal theory.