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On Probability and Moment Inequalities for Supermartingales and Martingales |
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| Authors: | S. V. Nagaev |
| Abstract: | The probability inequality for sum Sn= j=1nXj is proved under the assumption that the sequence Sk, k= , 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= . The well-known Burkholder moment inequality is deduced as a simple consequence. |
| Keywords: | filtered probability space expectation martingale supermartingale Burkholder inequality Bernstein and Bennet– Hoeffding inequalities Rosenthal inequality Fuk inequality separable Banach space |
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