Doob's martingale inequality

In mathematics, Doob's martingale inequality, also known as Kolmogorov’s submartingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a submartingale exceeds any given value over a given interval of time. As the name suggests, the result is usually given in the case that the process is a martingale, but the result is also valid for submartingales.

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