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- Publisher
- Springer Basel
- Copyright
- © Springer Basel 2013
- ISBN
- 978-3-0348-0489-9
- Pages
- 81 –93
- DOI
- 10.1007/978-3-0348-0490-5_6
- Publisher site
- See Chapter on Publisher Site
Abstract
[For any nonnegative Borel-measurable function f such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f(x)\;=\;0$$ \end{document} if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x\;=\;0$$ \end{document}, the best constant cf in the inequality \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$Ef(X\;-\;E\;X)\leqslant c_f E\;f(X)$$ \end{document} for all random variables X with a finite mean is obtained. Properties of the constant cf in the case when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f\;=\;|\cdot|^p$$ \end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$p>0$$ \end{document} are studied. Applications to concentration of measure in the form of Rosenthal-type bounds on the moments of separately Lipschitz functions on product spaces are given.]
Published: Apr 1, 2013
Keywords: Probability inequalities; Rosenthal-type inequalities; sums of independent random variables; martingales; concentration of measure; separately Lipschitz functions; product spaces