On convergence in variation of weakly convergent multidimensional distributions

DOI10.1134/S1064562415020039zbMath1432.60011OpenAlexW854934848MaRDI QIDQ492707

Vladimir I. Bogachev, Georgiĭ Il'ich Zelenov

Publication date: 21 August 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562415020039

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Convergence of probability measures (60B10) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (5)

Membership of distributions of polynomials in the Nikolskii-Besov class ⋮ On fractional regularity of distributions of functions in Gaussian random variables ⋮ Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy–Landau–Littlewood inequality ⋮ Fractional smoothness of images of logarithmically concave measures under polynomials ⋮ Distributions of polynomials in Gaussian random variables under constraints on the powers of variables

Cites Work

• Absolute continuity and convergence of densities for random vectors on Wiener chaos
• Convergence in variation of the joint laws of multiple Wiener-Itô integrals
• Convergence in total variation on Wiener chaos
• On measurable polynomials on infinite-dimensional spaces
• Distributional and \(L^q\) norm inequalities for polynomials over convex bodies in \(\mathbb{R}^n\)
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