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- W2898097210 abstract "In this note we give upper bounds on the quantiles of the one-sided maximum of a nonnegative submartingale in the class $Llog L$ or the maximum of a submartingale in $L^p$. Our upper bounds involve the entropy in the case of nonnegative martingales in the class $Llog L$ and the $L^p$-norm in the case of submartingales in $L^p$. Starting from our results on entropy, we also improve the so-called bounded differences inequality. All the results are based on optimal bounds for the conditional value at risk of real-valued random variables." @default.
- W2898097210 created "2018-11-02" @default.
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- W2898097210 date "2018-01-01" @default.
- W2898097210 modified "2023-10-18" @default.
- W2898097210 title "About Doob’s inequality, entropy and Tchebichef" @default.
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- W2898097210 doi "https://doi.org/10.1214/18-ecp178" @default.
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