Moments and ergodicity of the jump-diffusion CIR process

Abstract

We study the jump-diffusion CIR process, which is an extension of the Cox-Ingersoll-Ross model and whose jumps are introduced by a subordinator. We provide sufficient conditions on the Lévy measure of the subordinator under which the jump-diffusion CIR process is ergodic and exponentially ergodic, respectively. Furthermore, we characterize the existence of the κ-moment (κ>0) of the jump-diffusion CIR process by an integrability condition on the Lévy measure of the subordinator.