Moments and ergodicity of the jump-diffusion CIR process

TL;DR

This paper analyzes the jump-diffusion Cox-Ingersoll-Ross process, establishing conditions for ergodicity, exponential ergodicity, and moment existence based on the subordinator's Lévy measure.

Contribution

It provides new criteria for ergodic behavior and moment existence of the jump-diffusion CIR process, extending previous models with jump components.

Findings

Conditions for ergodicity and exponential ergodicity are derived.

Characterization of the existence of the $$-moment based on Lévy measure integrability.

Theoretical insights into the long-term behavior of jump-diffusion CIR processes.

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 L\'evy measure of the subordinator under which the jump-diffusion CIR process is ergodic and exponentially ergodic, respectively. Furthermore, we characterize the existence of the $\kappa$-moment ($\kappa>0$) of the jump-diffusion CIR process by an integrability condition on the L\'evy measure of the subordinator.