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Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching

  • Author Bio: zzzhang@dhu.edu.cn(ZhenzhongZhang); enhuazhang1993@163.com(EnhuaZhang); jytong@dhu.edu.cn(JinyingTong)
  • * Corresponding author: Jinying Tong.

    * Corresponding author: Jinying Tong.
The author Zhenzhong Zhang is supported by the Humanities and Social Sciences Fund of Ministry of Education of China (No. 17YJA910004). The author Jinying Tong is supported by the National Natural Science Foundation of China (Nos. 11401093 and 11471071).
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  • In this paper, we consider long time behavior of the Cox-Ingersoll-Ross (CIR) interest rate model driven by stable processes with Markov switching. Under some assumptions, we prove an ergodicity-transience dichotomy, namely, the interest rate process is either ergodic or transient. The sufficient and necessary conditions for ergodicity and transience of such interest model are given under some assumptions. Finally, an application to interval estimation of the interest rate processes is presented to illustrate our results.

    Mathematics Subject Classification: Primary: 60G52, 60J27.

    Citation:

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  • Figure 1.  Computer simulation of a single path of $X_t$ with initial value $X_0 = 0.3,r_0 = 1$ and different coefficients $\alpha = 1.25$(up), $\alpha = 1.75$(down)

    Figure 2.  Computer simulation of a single path of $X_t$ with initial value $X_0 = 0.3,r_0 = 1$ and $\alpha = 1.75$.

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