Geodesic
On distributions of homogeneous and convex functions in Gaussian random variables
Izvestiya. Mathematics , Tome 85 (2021) no. 5, pp. 852-882

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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. 
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     author = {V. I. Bogachev and E. D. Kosov and S. N. Popova},
     title = {On distributions of  homogeneous and convex functions in {Gaussian} random variables},
     journal = {Izvestiya. Mathematics },
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_5_a2/}
}
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V. I. Bogachev; E. D. Kosov; S. N. Popova. On distributions of  homogeneous and convex functions in Gaussian random variables. Izvestiya. Mathematics , Tome 85 (2021) no. 5, pp. 852-882. http://geodesic.mathdoc.fr/item/IM2_2021_85_5_a2/