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.
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