Geodesic
Distributions of Second Order Polynomials in Gaussian Random Variables
Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 67-79

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study bounds for the total variation distance between distributions of second order polynomials in normal random variables provided that they essentially depend on at least three variables. Moreover, we partially extend some recent bounds for the Kolmogorov distance between the distributions of norms of Gaussian random vectors to the case of the total variation distance.
Mots-clés : distribution of a polynomial, total variation distance
Keywords: Gaussian measure. 
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     author = {E. D. Kosov},
     title = {Distributions of {Second} {Order} {Polynomials} in {Gaussian} {Random} {Variables}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {67--79},
     publisher = {mathdoc},
     volume = {111},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a6/}
}
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E. D. Kosov. Distributions of Second Order Polynomials in Gaussian Random Variables. Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 67-79. http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a6/