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Distributions of polynomials in Gaussian random variables under constraints on the powers of variables. (English. Russian original) Zbl 1504.60005

Funct. Anal. Appl. 56, No. 2, 101-109 (2022); translation from Funkts. Anal. Prilozh. 56, No. 2, 29-38 (2022).
Summary: We study the densities of measures that are polynomial images of the standard Gaussian measure on \(\mathbb{R}^n\). We assume that the degree of a polynomial is fixed and each variable appears in the monomials of the polynomial to powers bounded by another fixed number.

MSC:

60A10 Probabilistic measure theory
60E05 Probability distributions: general theory
28A33 Spaces of measures, convergence of measures
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