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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Arras, Benjamin¹  Azmoodeh, Ehsan²  Poly, Guillaume³  Swan, Yvik⁴ 

[1] Sorbonne Univ, Lab Jacques Louis Lions, Paris, France

[2] Ruhr Univ Bochum, Fac Math, Bochum, Germany

[3] Univ Rennes 1, Inst Rech Math Rennes, Rennes, France

[4] Univ Liege, Math Dept, Liege, Belgium

关键词: Second Wiener chaos;    Variance-gamma distribution;    Wasserstein-2 distance;    Malliavin Calculus;    Stein discrepancy;   

DOI  :  10.1016/j.spa.2018.07.009

来源: Elsevier

【 摘 要 】

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of l(2)(N*). We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin-Peccati's Malliavin-Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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