Abstract:
We obtain broad conditions under which distributions of homogeneous
functions in Gaussian and more general random variables have bounded densities or even
densities of bounded variation or densities with finite Fisher information.
Analogous results are obtained for convex functions.
Applications to maxima of quadratic forms are given.
Keywords:
distribution density, quadratic form in Gaussian random variables, distribution of a homogeneous function.
This work was supported by the Russian Science Foundation,
grant no. 17-11-01058, at Lomonosov Moscow State University. The second author is a winner of the “Young Russian Mathematics” contest and thanks its sponsors and jury.
Citation:
V. I. Bogachev, E. D. Kosov, S. N. Popova, “On distributions of homogeneous and convex functions in Gaussian random variables”, Izv. Math., 85:5 (2021), 852–882
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\by V.~I.~Bogachev, E.~D.~Kosov, S.~N.~Popova
\paper On distributions of homogeneous and convex functions in Gaussian random variables
\jour Izv. Math.
\yr 2021
\vol 85
\issue 5
\pages 852--882
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Linking options:
https://www.mathnet.ru/eng/im9075
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This publication is cited in the following 2 articles:
E. D. Kosov, “Distributions of Second Order Polynomials in Gaussian Random Variables”, Math. Notes, 111:1 (2022), 71–81
V. I. Bogachev, “Chebyshev–Hermite polynomials and distributions of polynomials in Gaussian random variables”, Theory Probab. Appl., 66:4 (2022), 550–569
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