A bound on the Wasserstein-2 distance between linear combinations of independent random variables

DOI10.1016/j.spa.2018.07.009zbMath1481.60045arXiv1704.01376OpenAlexW2951431234WikidataQ129508897 ScholiaQ129508897MaRDI QIDQ2000150

Ehsan Azmoodeh, Benjamin Arras, Guillaume Poly, Yvik Swan

Publication date: 28 June 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.01376

zbMATH Keywords

Malliavin calculusStein discrepancysecond Wiener chaosvariance-gamma distributionWasserstein-2 distance

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Stochastic calculus of variations and the Malliavin calculus (60H07)

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Optimal Gamma Approximation on Wiener Space ⋮ A Stein characterisation of the generalized hyperbolic distribution ⋮ Stein's method for functions of multivariate normal random variables ⋮ Stein factors for variance-gamma approximation in the Wasserstein and Kolmogorov distances ⋮ The basic distributional theory for the product of zero mean correlated normal random variables ⋮ Bounding Kolmogorov distances through Wasserstein and related integral probability metrics ⋮ Unnamed Item ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ Some new Stein operators for product distributions ⋮ Bounds for an integral of the modified Bessel function of the first kind and expressions involving it ⋮ Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein's method. I ⋮ Weak convergence on Wiener space: targeting the first two chaoses ⋮ On a new Sheffer class of polynomials related to normal product distribution ⋮ On rate of convergence in non-central limit theorems ⋮ Stein characterizations for linear combinations of gamma random variables ⋮ Stability of higher order eigenvalues in dimension one ⋮ A unified approach to Stein's method for stable distributions ⋮ On algebraic Stein operators for Gaussian polynomials ⋮ Optimal variance-Gamma approximation on the second Wiener chaos

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