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Concentration Inequalities and Martingale Inequalities: A Survey

✍ Scribed by Chung, Fan; Lu, Linyuan


Book ID
121339123
Publisher
A K Peters Ltd
Year
2006
Tongue
English
Weight
431 KB
Volume
3
Category
Article
ISSN
1542-7951

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Let (X i ) be a martingale di erence sequence and let S n = n i=1 X i . Suppose (X i ) is bounded in L p . In the case p ¿ 2, Lesigne and Volnà y (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation (S n ¿ n) 6 cn -p=2 , which is optimal in a certain sense. In this article, we show that