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On Dobrushin’s inequality

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  • Szewczak, Zbigniew S.

Abstract

Lower and upper bounds in Dobrushin’s inequality for the variance of sums of functionals defined on a non-homogeneous Markov chain together with some related probability results are analyzed.

Suggested Citation

  • Szewczak, Zbigniew S., 2012. "On Dobrushin’s inequality," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1202-1207.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1202-1207
    DOI: 10.1016/j.spl.2012.02.019
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    References listed on IDEAS

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    1. Bradley, Richard C., 2011. "A note on two measures of dependence," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1823-1826.
    2. León, Carlos A., 2001. "Maximum asymptotic variance of sums of finite Markov chains," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 413-415, October.
    3. Szewczak, Zbigniew S., 2008. "Edgeworth expansions in operator form," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1583-1592, September.
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    Citations

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    Cited by:

    1. Alessandro Arlotto & J. Michael Steele, 2016. "A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1448-1468, November.
    2. Giuliano-Antonini, Rita & Szewczak, Zbigniew S., 2013. "An almost sure local limit theorem for Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 573-579.
    3. Szewczak, Zbigniew S., 2015. "A moment maximal inequality for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 129-133.

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