A note on martingale deviation bounds

Thomas R. Boucher

Statistics & Probability Letters, 2016, vol. 111, issue C, 8-11

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.

Keywords: Martingale; Martingale difference sequence; Deviations (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2015.12.030

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