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Hoeffding's inequality for uniformly ergodic Markov chains

Author

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  • Glynn, Peter W.
  • Ormoneit, Dirk

Abstract

We provide a generalization of Hoeffding's inequality to partial sums that are derived from a uniformly ergodic Markov chain. Our exponential inequality on the deviation of these sums from their expectation is particularly useful in situations where we require uniform control on the constants appearing in the bound.

Suggested Citation

  • Glynn, Peter W. & Ormoneit, Dirk, 2002. "Hoeffding's inequality for uniformly ergodic Markov chains," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 143-146, January.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:143-146
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    References listed on IDEAS

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    1. Balaji, S. & Meyn, S. P., 2000. "Multiplicative ergodicity and large deviations for an irreducible Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 123-144, November.
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    Cited by:

    1. Ankush Agarwal & Stefano De Marco & Emmanuel Gobet & Gang Liu, 2017. "Rare event simulation related to financial risks: efficient estimation and sensitivity analysis," Working Papers hal-01219616, HAL.
    2. Boucher, Thomas R., 2009. "A Hoeffding inequality for Markov chains using a generalized inverse," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1105-1107, April.
    3. Renou, Ludovic & Tomala, Tristan, 2015. "Approximate implementation in Markovian environments," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 401-442.
    4. Ahmad, I.A. & Amezziane, M., 2013. "Probability inequalities for bounded random vectors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1136-1142.
    5. Penev, Spiridon & Peng, Hanxiang & Schick, Anton & Wefelmeyer, Wolfgang, 2004. "Efficient estimators for functionals of Markov chains with parametric marginals," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 335-345, February.
    6. Chang, Hyeong Soo, 2006. "On convergence rate of the Shannon entropy rate of ergodic Markov chains via sample-path simulation," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1261-1264, July.
    7. Hunt, F.Y., 2005. "Sample path optimality for a Markov optimization problem," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 769-779, May.
    8. Miasojedow, Błażej, 2014. "Hoeffding’s inequalities for geometrically ergodic Markov chains on general state space," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 115-120.

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