Asymptotic development for the CLT in total variation distance

DOI10.3150/15-BEJ734zbMath1346.60016arXiv1407.0896MaRDI QIDQ726746

Vlad Bally, Lucia Caramellino

Publication date: 14 July 2016

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0896

zbMATH Keywords

central limit theoremintegration by partstotal variation distanceabstract Malliavin calculusregularizing functions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Convergence of probability measures (60B10)

Related Items (8)

Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ Total variation distance between stochastic polynomials and invariance principles ⋮ Normal approximation in total variation for statistics in geometric probability ⋮ Improved bounds for the total variation distance between stochastic polynomials ⋮ Kernel based Dirichlet sequences ⋮ Rényi divergence and the central limit theorem ⋮ A bound on the Wasserstein-2 distance between linear combinations of independent random variables ⋮ Regularization lemmas and convergence in total variation

Cites Work

• Absolute continuity and convergence of densities for random vectors on Wiener chaos
• Berry-Esseen bounds in the entropic central limit theorem
• Integration by parts formula and applications to equations with jumps
• Convergence in total variation on Wiener chaos
• An invariance principle under the total variation distance
• On the distances between probability density functions
• Normal Approximations with Malliavin Calculus
• On the central limit theorem in 𝑅_{𝑘}
• The Malliavin Calculus and Related Topics
• On Convergence in the Mean for Densities
• Real Analysis and Probability
• Analysis and Geometry of Markov Diffusion Operators
• Berry-Esseen bounds for the multi-dimensional central limit theorem

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