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Applications of geometric bounds to the convergence rate of Markov chains on

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  • Yuen, Wai Kong

Abstract

Quantitative geometric rates of convergence for reversible Markov chains are closely related to the spectral gap of the corresponding operator, which is hard to calculate for general state spaces. This article describes a geometric argumen t to give different types of bounds for spectral gaps of Markov chains on bounded subsets of and to compare the rates of convergence of different Markov chains.

Suggested Citation

  • Yuen, Wai Kong, 2000. "Applications of geometric bounds to the convergence rate of Markov chains on," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 1-23, May.
    • Handle: RePEc:eee:spapps:v:87:y:2000:i:1:p:1-23
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    References listed on IDEAS

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    1. Baxter, J. R. & Rosenthal, Jeffrey S., 1995. "Rates of convergence for everywhere-positive Markov chains," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 333-338, March.
    2. Amit, Y. & Grenander, U., 1991. "Comparing sweep strategies for stochastic relaxation," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 197-222, May.
    3. Amit, Yali, 1991. "On rates of convergence of stochastic relaxation for Gaussian and non-Gaussian distributions," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 82-99, July.
    4. Rosenthal, Jeffrey S., 1996. "Markov chain convergence: From finite to infinite," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 55-72, March.
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    Cited by:

    1. Aaron Smith, 2015. "Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1406-1430, December.
    2. Marie Vialaret & Florian Maire, 2020. "On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1349-1387, September.

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