On Probability and Moment Inequalities for Supermartingales and Martingales

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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Veröffentlicht in:Acta applicandae mathematicae 2003-10, Vol.79 (1-2), p.35
1. Verfasser: Nagaev, S V
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Inequality
Mathematical models
Probability
Random variables
Studies
Variance analysis
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Zusammenfassung: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