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Sharper bounds on the expectation of a strongly convex function of a random variable

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Název: Sharper bounds on the expectation of a strongly convex function of a random variable
Autoři: Ivelić Bradanović, Slavica
Informace o vydavateli: 2023.
Rok vydání: 2023
Témata: Jessen inequality, Converse Jensen inequality, Jensen inequality, Strongly convex functions, Edmundson-Madansky inequality
Popis: Jensen’s inequality is the most important inequality for convex functions. In the context of probability theory, Jensen’s inequality gives the lower bound on the expectation of a convex function of a random variable. On the other side, the upper bound is consequence of Converse Jensen's inequality, and is known as the Edmundson-Madansky inequality. In this work, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvement and generalization of Jensen’s inequality and its converse by means of the positive linear functionals acting on a space of real functions. As direct consequences we get sharper lower and upper bound on the expectation of a strongly convex function of a random variable.
Druh dokumentu: Conference object
Přístupové číslo: edsair.dris...01492..1fe0071526341080ba45a37def3cc05e
Databáze: OpenAIRE
Popis
Abstrakt:Jensen’s inequality is the most important inequality for convex functions. In the context of probability theory, Jensen’s inequality gives the lower bound on the expectation of a convex function of a random variable. On the other side, the upper bound is consequence of Converse Jensen's inequality, and is known as the Edmundson-Madansky inequality. In this work, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvement and generalization of Jensen’s inequality and its converse by means of the positive linear functionals acting on a space of real functions. As direct consequences we get sharper lower and upper bound on the expectation of a strongly convex function of a random variable.