The Well-Posedness and Ergodicity of a CIR Equation Driven by Pure Jump Noise

Xu Liu, Xingfu Hong, Fujing Tian, Chufan Xiao and Hao Wen ()
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Xu Liu: China Aerodynamics Research and Development Center, Mianyang 618000, China
Xingfu Hong: China Aerodynamics Research and Development Center, Mianyang 618000, China
Fujing Tian: China Aerodynamics Research and Development Center, Mianyang 618000, China
Chufan Xiao: China Aerodynamics Research and Development Center, Mianyang 618000, China
Hao Wen: China Aerodynamics Research and Development Center, Mianyang 618000, China

Mathematics, 2025, vol. 13, issue 12, 1-12

Abstract: The current paper is devoted to the dynamical property of the stochastic Cox–Ingersoll–Ross (CIR) model with pure jump noise, which is an extension of the CIR model. Firstly, we characterize the existence and 2-moment of the CIR process with a pure jump process. Consequently, we provide sufficient conditions for the compensated Poisson random measure under which the CIR process with a pure jump process is ergodic. Moreover, the stationary solution can be constructed from the invariant measure. Some numerical simulations are provided to visualize the theoretical results.

Keywords: CIR model; pure jump process; well-posedness; ergodicity; stationary solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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