Geodesic
Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 29-38

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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.
Mots-clés : distribution of a polynomial, total variation distance.
Keywords: distribution density, Kantorovich distance 
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     author = {E. D. Kosov},
     title = {Distributions of {Polynomials} in {Gaussian} {Random} {Variables} under {Constraints} on the {Powers} of {Variables}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {29--38},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a2/}
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E. D. Kosov. Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 29-38. http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a2/