Vladimir I. Bogachev, E. Kosov, Svetlana Nikolaevna Popova
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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 maxima of quadratic forms are given.
期刊介绍：
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to:
Algebra;
Mathematical logic;
Number theory;
Mathematical analysis;
Geometry;
Topology;
Differential equations.
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