7: Random Walks, Large Deviations, and Martingales
- Page ID
- 44631
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- 7.9: The Kolmogorov Inequalities
- We now use the previous theorems to establish Kolmogorov’s submartingale inequality, which is a major strengthening of the Markov inequality. Just as the Markov inequality in Section 1.7 was used to derive the Chebychev inequality and then the weak law of large numbers, the Kolmogorov submartingale inequality will be used to strengthen the Chebychev inequality, from which the strong law of large numbers will follow.
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