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A conditional version of Chebyshev’s other inequality

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Abstract

Under the conditions of integrability the conditional version E(f(X)G)E(g(X)|G) ≤ E(f(X)g(X)|G) a.s. of Chebyshev’s other inequality is proved for monotonic functions f and g of the samemonotonicity, for any random variable X, and for any σ-algebra G. An improved conditional version of the Grüss inequality is also proved.

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Authors and Affiliations

  1. Faculty of Physics and Mathematics, Moscow Region State University, ul. Radio 10A, Moscow, 105005, Russia

    N. Golikova & V. Kruglov

  2. Department of Statistics, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

    N. Golikova & V. Kruglov

Authors
  1. N. Golikova
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  2. V. Kruglov
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Correspondence to N. Golikova.

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Submitted by Andrei Volodin)

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Golikova, N., Kruglov, V. A conditional version of Chebyshev’s other inequality. Lobachevskii J Math 37, 404–408 (2016). https://doi.org/10.1134/S1995080216040077

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  • DOI: https://doi.org/10.1134/S1995080216040077

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