Long-term behavior of stochastic interest rate models with Markov switching

In this paper, we consider the long time behavior of Cox-Ingersoll-Ross (CIR) interest rate model with Markov switching. Using the ergodic theory of switching diffusions, we show that CIR model with Markov switching has a unique stationary distribution. Furthermore, we prove that the sequence X¯t:=1t∫0tXsds converges almost surely. As a by-product, we find that the marginal stationary distribution for CIR model with Markov switching can be determined uniquely by its moments.