Li, Huiyun; Chen, Xinjuan; Fu, Chunjuan; Li, Zhichan Improvement of Doob’s inequality. (Chinese. English summary) Zbl 1150.60421 J. Hebei Univ. Technol. 36, No. 2, 39-41 (2007). 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 Keywords:Doob’s inequality; Brownian motion; martingale Citations:Zbl 0554.60075 PDFBibTeX XMLCite \textit{H. Li} et al., J. Hebei Univ. Technol. 36, No. 2, 39--41 (2007; Zbl 1150.60421)