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.

中文翻译：

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关于高斯随机变量中齐次函数和凸函数的分布

我们获得了广泛的条件，在这些条件下，高斯和更一般的随机变量中的齐次函数分布具有有界密度，甚至有界变化的密度或具有有限 Fisher 信息的密度。对于凸函数获得了类似的结果。给出了二次型极大值的应用。