Abstract
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.
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