Necessary and sufficient conditions for ergodicity of CIR type SDEs with Markov switching

摘要

In this paper, we consider the ergodicity and transience of the Cox-Ingersoll-Ross (CIR) interest rate model with Markov switching. Using the theory of M-matrices, we give some necessary and sufficient conditions for ergodicity of the CIR interest rate model with Markov switching. Besides, we show that the transition semigroup converges to the stationary distribution at an exponential rate in the Wasserstein distance. Finally, two examples are presented to illustrate our theory.