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The Convergence of Nonhomogeneous Markov Chains in General State Spaces by the Coupling Method

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Abstract

We investigate the convergence of nonhomogeneous Markov chains in general state space by using the f norm and the coupling method, and thus, a sufficient condition for the convergence of nonhomogeneous Markov chains in general state space is obtained.

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References

  1. Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability. London: Springer Verlag, 2008

    MATH  Google Scholar 

  2. Kartashov N V. Inequalities in theorems of ergodicity and stability for Markov chains with common phase space, I. Probab Theor Appl, 1986, 30: 247–259

    Article  Google Scholar 

  3. Mukhamedov F. Weak ergodicity of nonhomogeneous Markov chains on noncom-mutative L1-spaces. Banach J Math Anal, 2013, 7: 53–73

    Article  MathSciNet  Google Scholar 

  4. Mukhamedov F. Ergodic properties of nonhomogeneous Markov chains dened on ordered Banach spaces with a base. Acta Math Hungar, 2015, 147: 294–323

    Article  MathSciNet  Google Scholar 

  5. Chen M F. From Markov Chains to Non-equilibrium Particle Systems. 2nd ed. Singapore: World Scientific, 2004

    Book  Google Scholar 

  6. Gong G L, Qian M P. A Course in Appied Stochastic Processes and Stochastic Models in Algorithms and Intelligence Computation. Beijing: Tsinghua University Press, 2004

    Google Scholar 

  7. Zhang S Y. The Existence and Application of Optimal Markow Coupling [D]. Beijing Normal University, 2000

  8. Zhu Z F, Zhang S Y. Study on the convergence of nonhomogeneous Markov chains with probability distance. Acta Mathematica Scientia, 2018, 38A(5): 963–969

    MathSciNet  MATH  Google Scholar 

  9. Lindvall T. Lectures on the Coupling Method. New York: Wiley, 1992

    MATH  Google Scholar 

  10. Zhu Z F, Zhang S Y. Study of f-exponent ergodic of Markov chains by coupling method. Acta Mathematica Sinica, 2019, (3): 287–292

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000, China

    Zhifeng Zhu  (朱志锋)

  2. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430081, China

    Zhifeng Zhu  (朱志锋)

  3. Hubei Key Laboratory of Applied Mathematics,School of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Shaoyi Zhang  (张绍义) & Fanji Tian  (田范基)

Authors
  1. Zhifeng Zhu  (朱志锋)
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  2. Shaoyi Zhang  (张绍义)
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  3. Fanji Tian  (田范基)
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Corresponding author

Correspondence to Fanji Tian  (田范基).

Additional information

Supported by Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y202003) and Hubei Education Department Foundation (B2019150) and Natural Science Foundation of Xiaogan (XGKJ2020010046).

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Zhu, Z., Zhang, S. & Tian, F. The Convergence of Nonhomogeneous Markov Chains in General State Spaces by the Coupling Method. Acta Math Sci 41, 1777–1787 (2021). https://doi.org/10.1007/s10473-021-0523-4

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  • DOI: https://doi.org/10.1007/s10473-021-0523-4

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