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Densities of distributions of homogeneous functions of Gaussian random vectors

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Abstract

We obtain broad sufficient conditions for the boundedness of distribution densities of homogeneous functions on spaces with Gaussian measures. Estimates for the distribution densities of maxima of quadratic forms are obtained.

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ACKNOWLEDGMENTS

We are grateful to A.N. Tikhomirov for useful discussions.

Funding

The second author is a winner of the “Young Russian Mathematics” contest and thanks its sponsors and jury. This work has been supported by the Russian Science Foundation Grant 17-11-01058 at Lomonosov Moscow State University.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    V. I. Bogachev & E. D. Kosov

  2. National Research University Higher School of Economics, 101000, Moscow, Russia

    V. I. Bogachev, E. D. Kosov & S. N. Popova

  3. St.-Tikhon’s Orthodox University, 115184, Moscow, Russia

    V. I. Bogachev

  4. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    S. N. Popova

Authors
  1. V. I. Bogachev
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  2. E. D. Kosov
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  3. S. N. Popova
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Corresponding authors

Correspondence to V. I. Bogachev or E. D. Kosov.

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Bogachev, V.I., Kosov, E.D. & Popova, S.N. Densities of distributions of homogeneous functions of Gaussian random vectors. Dokl. Math. 102, 460–463 (2020). https://doi.org/10.1134/S106456242006023X

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  • DOI: https://doi.org/10.1134/S106456242006023X

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