  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 L\'evy process $(J_t, t \ge 0)$. Under
some suitable conditions on the L\'evy measure of $(J_t, t \ge 0)$, we derive a
lower bound for the transition densities of the JCIR process. We also find some
sufficient condition guaranteeing the existence of a Forster-Lyapunov function
for the JCIR process, which allows us to prove its exponential ergodicity.
