Improved bounds for the total variation distance between stochastic polynomials

Egor Kosov and Anastasia Zhukova

Stochastic Processes and their Applications, 2024, vol. 170, issue C

Abstract: The paper studies upper bounds for the total variation distance between the distributions of two polynomials of a special form in random vectors satisfying the Doeblin-type condition. Our approach is based on the recent results concerning the Nikolskii–Besov-type smoothness of the distribution densities of polynomials in logarithmically concave random vectors. The main results of the paper improve the previously obtained estimates of Nourdin–Poly and Bally–Caramellino.

Keywords: Stochastic polynomial; Invariance principle; Logarithmically concave measure; Total variation distance; Distribution of a polynomial (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104279

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