On stability of the Markov-modulated skew CIR process

In this paper we consider the stability of a skew Cox–Ingersoll–Ross (CIR) process {Xt}t⩾0{Xt}t⩾0 whose parameters depend on a finite-state and irreducible continuous-time Markov chain {Jt}t⩾0{Jt}t⩾0. First, we prove the existence and uniqueness of the bivariate process {(Xt,Jt)}t⩾0{(Xt,Jt)}t⩾0 and derive the corresponding infinitesimal generator. Then we provide the stationary distribution equation of this bivariate process through their infinitesimal generator and as special cases, the explicit stationary distributions when JtJt has two or one state are calculated in the end.