On Probability and Moment Inequalities for Supermartingales and Martingales

The probability inequality for sum Sn=[summation operator]j=1nXj is proved under the assumption that the sequence Sk, k=$\overline{1,n}$, forms a supermartingale. This inequality is stated in terms of the tail probabilities P(Xj>y) and conditional variances of the random variables Xj, j=$\overlin...

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Bibliographic Details
Published inActa applicandae mathematicae Vol. 79; no. 1-2; p. 35
Main Author Nagaev, S V
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.10.2003
Subjects
Banach spaces
Inequality
Mathematical models
Probability
Random variables
Studies
Variance analysis
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Summary:The probability inequality for sum Sn=[summation operator]j=1nXj is proved under the assumption that the sequence Sk, k=$\overline{1,n}$, forms a supermartingale. This inequality is stated in terms of the tail probabilities P(Xj>y) and conditional variances of the random variables Xj, j=$\overline{1,n}$. The well-known Burkholder moment inequality is deduced as a simple consequence. [PUBLICATION ABSTRACT]
ISSN:0167-8019
1572-9036
DOI:10.1023/A:1025814306357