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On stability of the Markov-modulated skew CIR process

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  • Xu, Guangli
  • Wang, Yongjin

Abstract

In this paper we consider the stability of a skew Cox–Ingersoll–Ross (CIR) process {Xt}t⩾0 whose parameters depend on a finite-state and irreducible continuous-time Markov chain {Jt}t⩾0. First, we prove the existence and uniqueness of the bivariate process {(Xt,Jt)}t⩾0 and derive the corresponding infinitesimal generator. Then we provide the stationary distribution equation of this bivariate process through their infinitesimal generator and as special cases, the explicit stationary distributions when Jt has two or one state are calculated in the end.

Suggested Citation

  • Xu, Guangli & Wang, Yongjin, 2016. "On stability of the Markov-modulated skew CIR process," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 139-144.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:139-144
    DOI: 10.1016/j.spl.2015.10.020
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    References listed on IDEAS

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    1. Trutnau, Gerald, 2011. "Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1845-1863, August.
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    Cited by:

    1. Liu, Jiamin & Li, Zhao-Yan & Deng, Feiqi, 2021. "Asymptotic behavior analysis of Markovian switching neutral-type stochastic time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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