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A note on martingale deviation bounds

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  • Boucher, Thomas R.

Abstract

Let {Yi}i=1n be a martingale difference sequence and Sn=∑i=1nYi. Probability deviation bounds for martingale difference sequences generally focus on upper bounds for probabilities of large deviations P(Sn>λ), particularly of maxima of Sn. In this article bounds for probabilities of moderate deviations P(Sn<λ) are studied. The motivation is estimating the probability that the cumulative drift of a Markov chain is moderate, and thus estimates derived from sampling the chain are reliable.

Suggested Citation

  • Boucher, Thomas R., 2016. "A note on martingale deviation bounds," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 8-11.
    • Handle: RePEc:eee:stapro:v:111:y:2016:i:c:p:8-11
    DOI: 10.1016/j.spl.2015.12.030
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    References listed on IDEAS

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    1. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    2. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
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