In mathematics, Doob's martingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process 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 non-negative martingale, but the result is also valid for non-negative submartingales.
The inequality is due to the American mathematician Joseph Leo Doob.
Read more about Doob's Martingale Inequality: Statement of The Inequality, Further Inequalities, Related Inequalities, Application: Brownian Motion
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