On distributions of homogeneous and convex functions in Gaussian random variables

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...

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Bibliographic Details
Published inIzvestiya. Mathematics Vol. 85; no. 5; pp. 852 - 882
Main Authors Bogachev, V. I., Kosov, E. D., Popova, S. N.
Format Journal Article
LanguageEnglish
Published Providence London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.10.2021
IOP Publishing
Subjects
Convex analysis
distribution density
distribution of a homogeneous function
Fisher information
Mathematical analysis
quadratic form in Gaussian random variables
Quadratic forms
Random variables
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Summary: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.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM9075