A note on ergodicity for CIR model with Markov switching

AbstractRecently, Zhang et al. show that if ∑i=1Nπiβ(i)≠0, then the Cox-Ingersoll-Ross (CIR) model with Markov switching (see below, the SDE (1.2)) is ergodic in the Wasserstein distance if and only if ∑i=1Nπiβ(i)>0. In this article, we will show that if ∑i=1Nπiβ(i)=0, the Cox-Ingersoll-Ross (CIR) model with Markov switching is non-ergodic. Explicit expressions for the mean and variance of the CIR model with Markov switching are obtained. As a byproduct, the explicit expressions for mean of stationary distribution and second-order moments for such model are presented. Besides, we find the necessary and sufficient conditions of weak stationarity for CIR model with Markov switching.