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Rates of convergence for everywhere-positive Markov chains

Author

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  • Baxter, J. R.
  • Rosenthal, Jeffrey S.

Abstract

We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:4:p:333-338
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    Cited by:

    1. Mandel, Antoine & Veetil, Vipin P., 2021. "Monetary dynamics in a network economy," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    2. 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.
    3. Lukka Tuomas J. & Kujala Janne V., 2002. "Using Genetic Operators to Speed up Markov Chain Monte Carlo Integration," Monte Carlo Methods and Applications, De Gruyter, vol. 8(1), pages 51-72, December.
    4. Claudio Asci, 2009. "Generating Uniform Random Vectors in Z p k : The General Case," Journal of Theoretical Probability, Springer, vol. 22(3), pages 791-809, September.
    5. Nielsen, Adam, 2016. "The Monte Carlo computation error of transition probabilities," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 163-170.
    6. Sairam Rayaprolu & Zhiyi Chi, 2021. "False Discovery Variance Reduction in Large Scale Simultaneous Hypothesis Tests," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 711-733, September.
    7. Hernández-Lerma, Onésimo & Lasserre, Jean B., 1996. "Existence of bounded invariant probability densities for Markov chains," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 359-366, August.
    8. Rosenthal, Jeffrey S., 1996. "Markov chain convergence: From finite to infinite," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 55-72, March.
    9. Claudio Asci, 2001. "Generating Uniform Random Vectors," Journal of Theoretical Probability, Springer, vol. 14(2), pages 333-356, April.
    10. Anton Molyboha & Michael Zabarankin, 2011. "Optimization of steerable sensor network for threat detection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 564-577, September.

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