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Ergodicity of regime-switching diffusions in Wasserstein distances

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  • Shao, Jinghai

Abstract

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to justify the convergence of the regime-switching diffusion processes in Wasserstein distances. The cost function we used to define the Wasserstein distance is not necessarily bounded. The continuous time Markov chains with finite and infinite countable state space are all studied. To deal with the infinite countable state space, we put forward a finite partition method. The boundedness for state-dependent regime-switching diffusions in an infinite countable state space is also studied.

Suggested Citation

  • Shao, Jinghai, 2015. "Ergodicity of regime-switching diffusions in Wasserstein distances," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 739-758.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:2:p:739-758
    DOI: 10.1016/j.spa.2014.10.007
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    References listed on IDEAS

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    1. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    2. Mao, Yong-Hua, 2006. "Convergence rates in strong ergodicity for Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1964-1976, December.
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    Cited by:

    1. Cappelletti, Daniele & Pal Majumder, Abhishek & Wiuf, Carsten, 2021. "The dynamics of stochastic mono-molecular reaction systems in stochastic environments," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 106-148.
    2. Shao, Jinghai & Wang, Lingdi & Wu, Qiong, 2023. "Ergodicity and stability of hybrid systems with piecewise constant type state-dependent switching," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 1-23.
    3. Xinghu Jin & Tian Shen & Zhonggen Su, 2023. "Using Stein’s Method to Analyze Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1797-1828, September.

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