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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Exponential upper bounds for sums of martingale differences

Let $(X_{i})_{i\geq 1}$ be a sequence of centered real-valued martingale-differences with respect to some filtration $(\mathcal{F}_{i})_{i \geq 1}$. Define $S_{n} = \sum_{i=1}^{n}X_{i}$ and $\Sigma^{2 …