On Properties of Polynomials in Random Elements

DOI10.1137/S0040585X97T987673zbMath1381.60015arXiv1605.05282OpenAlexW2962795226MaRDI QIDQ2811901

Vladimir V. Ulyanov

Publication date: 8 June 2016

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.05282

zbMATH Keywords

Vinogradov mean value theoremstability problemdistribution tailscharacterization problemdistribution of quadratic formsCantor distributionsingular distributionsbounds for characteristics functionpolynomials in random elements

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Probability theory on linear topological spaces (60B11)

Related Items

Chebyshev--Hermite Polynomials and Distributions of Polynomials in Gaussian Random Variables, On Bounds for Characteristic Functions of Powers of Asymptotically Normal Variables, Distributions of polynomials in Gaussian random variables under constraints on the powers of variables

Cites Work

• Vinogradov's mean value theorem via efficient congruencing
• Edgeworth expansions in functional limit theorems
• On mean values of the modulus of a trigonometric sum
• Near-optimal mean value estimates for multidimensional Weyl sums
• Some Approximation Problems in Statistics and Probability
• On Gaussian Measure of Balls in a Hilbert Space
• Asymptotic expansions for bivariate von Mises functionals
• On Singular Monotonic Functions of the Cantor Type
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