AN INEQUALITY FOR EXPECTATION OF MEANS OF POSITIVE RANDOM VARIABLES

被引：4
作者：
Gibilisco, Paolo [1 ]
Hansen, Frank [2 ]
机构：
[1] Univ Roma Tor Vergata, Dept Econ & Finance, Via Columbia 2, I-00133 Rome, Italy
[2] Tohoku Univ, Inst Excellence Higher Educ, Sendai, Miyagi, Japan
来源：
ANNALS OF FUNCTIONAL ANALYSIS | 2017年 / 8卷 / 01期
关键词：
numerical means; operator means; concavity; random matrices; PERSPECTIVES; MATRICES;
D O I：
10.1215/20088752-3750087
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Suppose that X, Y are positive random variables and m is a numerical (commutative) mean. We prove that the inequality E(m(X, Y)) <= m(E(X), E(Y)) holds if and only if the mean is generated by a concave function. With due changes we also prove that the same inequality holds for all operator means in the Kubo Ando setting. The case of the harmonic mean was proved by C. R. Rao and B. L. S. Prakasa Rao.
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页码：142 / 151
页数：10
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