(Quasi)additivity properties of the Legendre--Fenchel transform and its inverse, with applications in probability

zbMath1384.26034arXiv1305.1860MaRDI QIDQ4604052

Iosif Pinelis

Publication date: 23 February 2018

Full work available at URL: https://arxiv.org/abs/1305.1860

zbMATH Keywords

quantilesexponential inequalitiesprobability inequalitiesLegendre-Fenchel transformsums of random variablesexponential rate functionCramer-Chernoff functionHölder convolution

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48)

Cites Work

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• On McDiarmid's concentration inequality
• Local invariance principles and their application to density estimation
• On the Bennett-Hoeffding inequality
• Asymptotic Theory of Weakly Dependent Random Processes
• Exact Exponential Bounds for Sums of Independent Random Variables
• A Simple Proof of the Holder and the Minkowski Inequality

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