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Improvement of Doob’s inequality. (Chinese. English summary) Zbl 1150.60421

Summary: Doob’s inequality for \(p=1\) is improved. The lower bound is estimated without \(X_0\equiv1\) in R. Durrett [Brownian motion and martingales in analysis, Wadsworch Inc., California (1984; Zbl 0554.60075)], and the coefficient of the upper bounded is reduced from \(\frac{e}{e-1}\) to 1. So, the coefficient of the central part is identical. Finally, an example of B.M. shows that the coefficient can’t be improved again.

MSC:

60J65 Brownian motion
60E15 Inequalities; stochastic orderings

Citations:

Zbl 0554.60075
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