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Improved bounds for the total variation distance between stochastic polynomials

Stochastic Processes and their Applications. 2024. Vol. 170. Article 104279.
Kosov E., Zhukova A.

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.

Research target: Mathematics
Language: English
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Text on another site
Keywords: invariance principleTotal variation distanceLogarithmically concave measureDistribution of a polynomialStochastic polynomial
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