Exponential ergodicity of the jump-diffusion CIR process

In this paper we study the jump-diffusion CIR process (shorted as JCIR), which is an extension of the classical CIR model. The jumps of the JCIR are introduced with the help of a pure-jump Levy process (J(t), t >= 0). Under some suitable conditions on the Levy measure of (J(t), t >= 0), we derive a lower bound for the transition densities of the JCIR process. We also find some sufficient conditions under which the function V(x) = x, x >= 0, is a Forster-Lyapunov function for the JCIR process. This allows us to prove that the JCIR process is exponentially ergodic.