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Hoeffding’s inequalities for geometrically ergodic Markov chains on general state space

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  • Miasojedow, Błażej

Abstract

Let (Xn)n≥1 be a Markov chain on a general state space with stationary distribution π and a spectral gap in the space Lπ2. In this paper, we prove that the probabilities of large deviations of sums Sn=∑k=1nf(Xk) satisfy an inequality of Hoeffding type. We generalize results of León and Perron (2004) in two directions; in our paper the state space is general and we do not assume reversibility.

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  • 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.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:115-120
    DOI: 10.1016/j.spl.2014.01.013
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Sandrić, Nikola & Šebek, Stjepan, 2023. "Hoeffding’s inequality for non-irreducible Markov models," Statistics & Probability Letters, Elsevier, vol. 200(C).
    2. Koch, Erwan & Robert, Christian Y., 2019. "Geometric ergodicity for some space–time max-stable Markov chains," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 43-49.
    3. Fan, Jianqing & Guo, Yongyi & Jiang, Bai, 2022. "Adaptive Huber regression on Markov-dependent data," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 802-818.

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