Integro-differential equations and functional analysis

On distributions of trigonometric polynomials in Gaussian random variables

G. I. Zelenov<sup>ab

a</sup> Lomonosov Moscow State University, Moscow, Russian Federation
^b Higher School of Economics, Moscow, Russian Federation

Abstract: We prove new results about the inclusion of distributions of trigonometric polynomials in Gaussian random variables to Nikolskii–Besov classes. In addition, we estimate the total variance distances between distributions of trigonometric polynomials via the $L^q$-distances between the polynomials themselves.

Keywords: Nikolskii–-Besov class, Gaussian measure, distribution of a trigonometric polynomial.

UDC: 519.2

MSC: 60E05, 60E015, 28C20, 60F99

Received: 05.06.2021

Language: English

DOI: 10.26516/1997-7670.2021.37.77

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