Some properties of doubly skewed CIR processes

In this paper, we investigate some properties of the doubly skewed CIR process which is an extension of skew Brownian motion. The weak existence and pathwise uniqueness of this process is considered in the beginning. Then we present the explicit formulae for the stationary density function and show that the process is positive Harris recurrent and geometrically ergodic. We also provide the explicit Laplace transforms of the first hitting times by using the basic theory of linear diffusions. As a natural corollary, the expectations of the first hitting times are given in the end.