Some Characterizations Of Stable Processes With Markov Switching

In this paper,we mainly discuss the Harnack inequality for the switching sta-ble process and some characterizations for the Cox-Ingersoll-Ross(CIR)model with Markov switching.Motivated by the Harnack inequality for the pure jump process,we establish the Harnack inequality for a class of stochastic differential equations driven by the ?-stable process with Markov switching.Then,the expectation and covariance for the Cox-Ingersoll-Ross(CIR)model with Markov switching are discussed.Explicit expressions for the covariance function of the CIR model with Markov switching are given.