Exponential ergodicity of CIR interest rate model with random switching

In this paper, we consider ergodicity of Cox–Ingersoll–Ross (CIR) interest rate model with random switching. First, we show that the CIR model with switching has a unique stationary distribution. Next, we prove that the transition semigroup for the CIR model with switching converges to the stationary distribution at an exponential rate in the Wasserstein distance. Moreover, under two particular cases, the explicit expressions for stationary distributions are presented. Finally, the central limit theorem for the CIR model with random switching is established.