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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 91, 2019 - Issue 7: Hammamet Stochastic Analysis 2017
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Articles

Moments and ergodicity of the jump-diffusion CIR process

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Pages 974-997 | Received 19 Jan 2018, Accepted 28 Jan 2019, Published online: 08 Feb 2019
 

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.

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Acknowledgements

We are very grateful to the anonymous referees, whose valuable comments have led to an improvement of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

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