Blackwell, D. Large deviations for martingales. (English) Zbl 0883.60041 Pollard, David (ed.) et al., Festschrift for Lucien Le Cam: research papers in probability and statistics. New York, NY: Springer. 89-91 (1997). The following two exponential maximal inequalities are proved for a martingale \(S_0,S_1,\dots\) with \(S_0=0\) and \(|S_n-S_{n-1}|\leq1\) a.s. If \(a,b,c\geq0\), then \[ P\{S_n\geq a+bn\text{ for some }n\}\leq\exp(-2ab),\qquad P\{S_n\geq cn\text{ for some }n\geq N\}\leq r_1^N\leq r_2^N, \] where \(r_1=((1+c)^{1+c}(1-c)^{1-c})^{-1/2}\) and \(r_2=\exp(-c^2/2)\).For the entire collection see [Zbl 0861.00032]. Reviewer: A.Schied (Berlin) Cited in 2 Documents MSC: 60G42 Martingales with discrete parameter 60F10 Large deviations Keywords:maximal inequalities; martingales with bounded increments PDFBibTeX XMLCite \textit{D. Blackwell}, in: Festschrift for Lucien Le Cam: research papers in probability and statistics. New York, NY: Springer. 89--91 (1997; Zbl 0883.60041)