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Probability of Random Vector Hitting a Polyhedral Cone: Majorization Aspect

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Abstract

The paper presents conditions under which the probability of a linear combination of random vectors hitting into a polyhedral cone is a Schur-concave function of the coefficients of the combination. It is required that the cone contains the point 0, its edges are parallel to the coordinate axes, and the distribution density of the vectors is a logarithmically concave sign-invariant function.

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ACKNOWLEDGMENTS

The author is grateful to Dr. V. Solev for useful consultations.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, 191023, St.Petersburg, Russia

    M. I. Revyakov

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  1. M. I. Revyakov
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Correspondence to M. I. Revyakov.

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Revyakov, M.I. Probability of Random Vector Hitting a Polyhedral Cone: Majorization Aspect. Vestnik St.Petersb. Univ.Math. 55, 321–328 (2022). https://doi.org/10.1134/S106345412203013X

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  • DOI: https://doi.org/10.1134/S106345412203013X

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